absolute stability of third order systems a numerical algorithm the problem of absolute stability is one of the oldest open problems in the theory of control even for the particular case of second order systems a complete solution was presented only very recently for third order systems the most general theoretical results were obtained by barabanov he derived an implicit characterization of the most destabilizing nonlinearity using a variational approach in this paper we show that his approach yields a simple and efficient numerical scheme for solving the problem in the case of third order systems this allows the determination of the critical value where stability is lost in a tractable and accurate fashion this value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

a fast semi discrete kansa method to solve the two dimensional spatiotemporal fractional diffusion equation abstract fractional order diffusion equations fdes extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media real world diffusion can be multi dimensional requiring efficient numerical solvers that can handle long term memory embedded in mass transport to address this challenge a semi discrete kansa method is developed to approximate the two dimensional spatiotemporal fde where the kansa approach first discretizes the fde then the gauss jacobi quadrature rule solves the corresponding matrix and finally the mittag leffler function provides an analytical solution for the resultant time fractional ordinary differential equation numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes applications further show that the numerical method can efficiently solve two dimensional spatiotemporal fde models with either a continuous or discrete mixing measure hence this study provides an efficient and fast computational method for modeling super diffusive sub diffusive and mixed diffusive processes in large two dimensional domains with irregular shapes

brief paper root mean square gains of switched linear systems a variational approach we consider the problem of computing the root mean square rms gain of switched linear systems we develop a new approach which is based on an attempt to characterize the worst case switching law wcsl that is the switching law that yields the maximal possible gain our main result provides a sufficient condition guaranteeing that the wcsl can be characterized explicitly using the differential riccati equations dres corresponding to the linear subsystems this condition automatically holds for first order siso systems so we obtain a complete solution to the rms gain problem in this case

shape optimization using reproducing kernel particle method and an enriched genetic algorithm combining reproducing kernel particle method rkpm with the proposed multi family genetic algorithm mfga a novel approach to continuum based shape optimization problems is brought forward in this paper taking full advantage of the features of meshfree method and the merits of mfga the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely the effectiveness versatility and performance of the proposed approach are demonstrated via three 2 d numerical examples

the structure of time optimal trajectories for single input systems in the plane the general real analytic case for arbitrary single input real analytic systems in the plane in which the control enters linearly we prove that the time optimal trajectories are finite concatenations of bang bang and singular arcs with local bounds on the number of switchings no nondegeneracy assumption is made other than real analyticity the analysis proceeds by applying our previous results on nondegenerate c infty systems to study the behavior of the trajectories on a neighborhood of every point except for the points in a discrete set of branch points the branch points are then handled by a combination of control theoretic arguments and the use of subanalytic set theory

a nodal integration and post processing technique based on voronoi diagram for galerkin meshless methods a stabilized nodal integration technique is adopted by adding the square of the residual of the equilibrium equation to the potential energy functional an approach is proposed based on voronoi diagram to evaluate nodal volumes accurately it is a key issue for nodal integration of galerkin meshless methods furthermore as the dual of voronoi diagram the corresponding delaunay triangles are at hand provided voronoi diagram construction is completed a realistic technique is proposed based on background delaunay triangles for post processing of meshless results in the whole domain of interest two elastic stress analysis problems are investigated which demonstrate the approach is realistic versatile and robust

the structure of time optimal trajectories for single input systems in the plane the c nonsingular case for single input c infty systems in the plane in which the control enters linearly we prove if the system is suitably nondegenerate that the time optimal trajectories are finite concatenations of bang bang and singular arcs with local bounds on the number of switchings

a subdomain collocation method based on voronoi domain partition and reproducing kernel approximation a subdomain collocation reproducing kernel approximation method is proposed subdomains are constructed by nonoverlapping voronoi cells and a local weak form is defined over these subdomains the standard rkpm shape functions are used directly for approximation while weighting functions of the subdomain collocation method hold a constant value of unit only over a specific voronoi cell the body integration of the local weak form is now converted into much cheaper and efficient contour integration along the boundaries of voronoi cells it does not need to impose traction free boundary conditions explicitly in contrast to point collocation method furthermore the method provides a natural background structure for performing h adaptivity analysis straightforwardly all these features constitute the subdomain collocation method a promising alternative to standard galerkin method and point collocation method some elastostatics examples are presented to demonstrate the effectiveness the convergence property and the adaptivity performance of present method

a switched state feedback law for the stabilization of lti systems inspired by prior work in the design of switched feedback controllers for second order systems we develop a switched state feedback control law for the stabilization of linear time invariant lti systems of arbitrary dimension the control law operates by switching between two static gain vectors in such a way that the state trajectory is driven onto a stable n 1 dimensional hyperplane where n represents the system dimension we begin by briefly examining relevant geometric properties of the phase portraits in the case of two dimensional systems to develop intuition and we then show how these geometric properties can be expressed as algebraic constraints on the switched vector fields that are applicable to lti systems of arbitrary dimension we then derive necessary and sufficient conditions to ensure stabilizability of the resulting switched system using the proposed approach characterized primarily by simple conditions on eigenvalues and describe an explicit procedure for designing stabilizing controllers we then show how the newly developed control law can be applied to the problem of minimizing the maximal lyapunov exponent of the corresponding closed loop state trajectories and we illustrate the closed loop transient performance of these switched state feedback controllers via multiple examples

a condition for the stability of switched nonlinear systems in this paper we present a sufficient condition for the global asymptotic stability of a switched nonlinear system composed of a finite family of subsystems we show that the global asymptotic stability of each subsystem and the pairwise commutation of the vector fields that define the subsystems i e the lie bracket of any pair of them is zero are sufficient for the global asymptotic stability of the switched system we also show that these conditions are sufficient for the existence of a common lyapunov function

on the analysis of nonlinear nilpotent switched systems using the hall sussmann system abstract we consider an open problem on the stability of nonlinear nilpotent switched systems posed by daniel liberzon partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems the global structure is crucial in establishing stability we show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system the nilpotent hall sussmann system furthermore local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems we derive several new results revealing the elegant lie algebraic structure of the nilpotent hall sussmann system

radial spline collocation method for static analysis of beams conventional spline collocation method scm uses equally spaced knots in the computation of approximation however when load distribution geometry material property of structure are discontinuous it will greatly reduce accuracy the goal of this paper is mainly to develop unequally spaced knots to improve the disadvantage of using equally spaced knots applying the concept of radial basis functions rbf the spline function is transformed into radial spline function rsf consequently rsf can conveniently calculate the values for unequally spaced knots so that the complicated beam problems with discontinuous characteristics can be solved accurately and efficiently by the proposed radial spline collocation method rscm in this paper the proposed rscm also can be extended to solve other structural problems such as frame plate shell etc

a natural neighbour method for linear elastic problems based on fraeijs de veubeke variational principle the natural neighbour method can be considered as belonging to the meshless methods classically the development of this method is based on the virtual work principle in the present paper we use the natural neighbour method for 2d domains starting from the fraeijs de veubeke variational principle and we approximate separately the displacement field the stress field and the strain field the assumed strains and the assumed stresses are constant over each voronoi cell the assumed surface reactions are constant along the edge where the displacements are imposed while the assumed displacements are interpolated by laplace interpolants in the absence of body forces it is shown that the calculation of integrals on the area of the solid domain can be avoided only integrals on the edges of the voronoi cells are necessary on the other hand displacements can be imposed in the average sense on some boundaries of the domain patch tests and some applications in the elastic domain are given in the paper and show the effectiveness of the method copyright 2007 john wiley sons ltd

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

characterising the stabilisability for second order linear switched systems the stabilisability of second order linear switched systems is the topic focused on in a number of papers however some of its fundamental characteristics are still unrevealed in this article regarding a pair of subsystems we are interested in characterising this problem from both the state triggering and time domain viewpoints and in revealing the inherent connection between them to this end we first use polar coordinates to represent the geometric property of switching and the dynamical behaviours caused by it and then put the geometrised switching control into correspondence with the implicit stabilisation mechanism behind it doing this in a strong way relies on classifying switching control into two types intuitively namely chattering switching and spinning switching and then clarifying their distinction and properties rigorously furthermore the uniform convergence of the forced trajectory is shown by presenting estimation on its decay rate and the limit cycles and sliding motions genera

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

a fe meshfree quad4 element based on partition of unity a new 4 node quadrilateral element is developed by combining the shape functions of finite element and meshfree methods the objective is to synergise the attractive features of finite element and meshfree shape functions using the concepts of partition of unity pu methods the shape functions of the well known quad4 element are used for pu and the least square point interpolation for local approximation this enables the proposed element inherit the compatibility properties of finite element method and the quadratic polynomial completeness properties of meshfree methods numerical results for the bench mark problems show that the proposed element has a good tolerance to distorted meshes the element also seems to be free from the linear dependence problem which is known to plague some of the pu based elements

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

transition time optimization for switched mode dynamical systems this note considers the problem of determining optimal switching times at which mode transitions should occur in multimodal hybrid systems it derives a simple formula for the gradient of the cost functional with respect to the switching times and uses it in a gradient descent algorithm much of the analysis is carried out in the setting of optimization problems involving fixed switching mode sequences but a possible extension is pointed out for the case where the switching mode sequence is a part of the variable numerical examples testify to the viability of the proposed approach

numerical solution to the unsteady two dimensional schrodinger equation using meshless local boundary integral equation method a meshless local boundary integral equation lbie method is proposed to solve the unsteady two dimensional schrodinger equation the method is based on the lbie with moving least squares mls approximation for the mls approximation nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables a time stepping method is employed to deal with the time derivative an efficient method for dealing with singular domain integrations that appear in the discretized equations is presented finally numerical results are considered for some examples to demonstrate the accuracy efficiency and high rate of convergence of this method copyright 2008 john wiley sons ltd

a local point interpolation method for static and dynamic analysis of thin beams abstract the local point interpolation method lpim is a newly developed truly meshless method based on the idea of meshless local petrov galerkin mlpg approach in this paper a new lpim formulation is proposed to deal with fourth order boundary value and initial value problems for static and dynamic analysis stability free vibration and forced vibration of beams local weak forms are developed using weighted residual method locally in order to introduce the derivatives of the field variable into the interpolation scheme a technique is proposed to construct polynomial interpolation with kronecker delta function property based only on a group of arbitrarily distributed points because the shape functions so obtained possess delta function property the essential boundary conditions can be implemented with ease as in the conventional finite element method fem the validity and efficiency of the present lpim formulation are demonstrated through numerical examples of beams under various loads and boundary conditions

a point collocation method based on reproducing kernel approximations a reproducing kernel particle method with built in multiresolution features in a very attractive meshfree method for numerical solution of partial differential equations the design and implementation of a galerkin based reproducing kernel particle method however faces several challenges such as the issue of nodal volumes and accurate and efficient implementation of boundary conditions in this paper we present a point collocation method based on reproducing kernel approximations we show that in a point collocation approach the assignment of nodal volumes and implementation of boundary conditions are not critical issues and points can be sprinkled randomly making the point collocation method a true meshless approach the point collocation method based on reproducing kernel approximations however requires the calculation of higher order derivatives that would typically not be required in a galerkin method a correction function and reproducing conditions that enable consistency of the point collocation method are derived the point collocation method is shown to be accurate for several one and two dimensional problems and the convergence rate of the point collocation method is addressed copyright 2000 john wiley sons ltd

stability analysis of second order switched homogeneous systems we study the stability of second order switched homogeneous systems using the concept of generalized first integrals we explicitly characterize the most destabilizing switching law and construct a lyapunov function that yields an easily verifiable necessary and sufficient condition for asymptotic stability using the duality between stability analysis and control synthesis this also leads to a novel algorithm for designing a stabilizing switching controller

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

brief paper a second order maximum principle for discrete time bilinear control systems with applications to discrete time linear switched systems a powerful approach for analyzing the stability of continuous time switched systems is based on using optimal control theory to characterize the most unstable switching law this reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific most unstable switching law for discrete time switched systems the variational approach received considerably less attention this approach is based on using a first order necessary optimality condition in the form of a maximum principle mp and typically this is not enough to completely characterize the most unstable switching law in this paper we provide a simple and self contained derivation of a second order necessary optimality condition for discrete time bilinear control systems this provides new information that cannot be derived using the first order mp we demonstrate several applications of this second order mp to the stability analysis of discrete time linear switched systems

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

novel adaptive meshfree integration techniques in meshless methods summary we propose two strategies of novel adaptive numerical integration based on mapping techniques for solving the complicated problems of domain integration encountered in meshfree methods several mapping methods are presented in detail that map a complex integration domain to much simpler ones for example squares triangles or circles the techniques described in the paper can be applied to both global and local weak forms and the highly nonlinear meshfree integrands are evaluated with controlled accuracy the necessity of the clumsy procedure of background mesh or cell structures used for integration purpose in existing meshfree methods is avoided and many meshfree methods that require the domain integration can now become truly meshfree various numerical examples in two dimensions are considered to demonstrate the applicability and the effectiveness of the proposed methods and it shows that the accuracy is improved significantly their obtained results are compared with analytical solutions and other approaches and very good agreements are found additionally some three dimensional cases applied by the present methods are also examined copyright 2012 john wiley sons ltd

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

non linear version of stabilized conforming nodal integration for galerkin mesh free methods a stabilized conforming sc nodal integration which meets the integration constraint in the galerkin meshfree approximation is generalized for nonlinear problems in sc nodal integration a strain smoothing stabilization is introduced and applied to the deformation gradient using a lagrangian meshfree discretization the assumed strain method expressed in terms of deformation gradient is employed to formulate an efficient meshfree discrete equation for nonlinear problems a significant gain in computational efficiency is achieved as well as enhanced accuracy in comparison to the solution of meshfree method using gauss integration method the performance of the proposed method appears to be quite robust when dealing with irregular discretization

operator content of the ashkin teller quantum chain superconformal and zamolodchikov fateev invariance ii boundary conditions compatible with the torus for pt i see ibid vol 20 no 8 p l479 85 1987 the authors present the operator content of the ashkin teller quantum chain with eight boundary conditions corresponding to the eight elements of the group d4 which gives the global symmetry of the system this operator content is a conjecture based on an extensive numerical study and was proven to be correct at the ising decoupling point for the values of the coupling constant where n 2 superconformal invariance was seen for free boundary conditions the situation is now more complex one finds sectors which have n 2 and n 1 superconformal invariance and sectors which have no superconformal invariance at all if however they combine the wrong sectors of the spectra which correspond to two different values of the coupling constant a new symmetry shows up they also analyse the operator content at the fateev zamolodchikov points here the wrong sectors can be described by a few new primary fields

implementation of meshless lbie method to the 2d non linear sg problem in this paper the meshless local boundary integral equation lbie method for numerically solving the non linear two dimensional sine gordon sg equation is developed the method is based on the lbie with moving least squares mls approximation for the mls nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables the approximation functions are constructed entirely using a set of scattered nodes and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of method to deal with the unsteady non linear problems in large domains copyright 2009 john wiley sons ltd

sliding mode control of discrete time switched systems with repeated scalar nonlinearities this note studies the design of sliding mode control smc for discrete time hybrid stochastic switched systems with repeated scalar nonlinearities the weighed mathcal h infty gain performance is considered for the system dynamics to optimize its transient state performance first sufficient conditions are given to guarantee the corresponding system is exponentially stable while achieving a desired weighed mathcal h infty performance a new switching surface function is constructed by the average dwell time technique and the positive diagonally dominant lyapunov functional method to further reduce the conservativeness induced by the repeated scalar nonlinearity then the corresponding sliding mode dynamics are obtained and the solvability condition for the desired switching surface function is derived furthermore the synthesis of the proposed smc law is proposed to force the resulting closed loop system trajectories onto the pre specified sliding mode region with a desired level of accuracy finally the feasibility and the effectiveness of the presented new design techniques are illustrated by examples and simulations

the natural neighbour petrov galerkin method for elasto statics in this paper an efficient and accurate meshless natural neighbour petrov galerkin method nnpg is proposed to solve elasto static problems in two dimensional space this method is derived from the generalized meshless local petrov galerkin method mlpg as a special case in the nnpg the local supported trial functions are constructed based on the non sibsonian interpolation and test functions are taken as the three node triangular fem shape functions the local weak forms of the equilibrium equation and the boundary conditions are satisfied in local polygonal sub domains these sub domains are constructed with delaunay tessellations and domain integrals are evaluated over included delaunay triangles by using gaussian quadrature scheme as this method combines the advantages of natural neighbour interpolation with petrov galerkin method together no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions several numerical examples are presented and the results show the presented method is easy to implement and very accurate for these problems copyright 2005 john wiley sons ltd

continuous discrete time observer design for lipschitz systems with sampled measurements this technical note concerns observer design for lipschitz nonlinear systems with sampled output using reachability analysis an upper approximation of the attainable set is given when this approximation is formulated in terms of a convex combination of linear mappings a sufficient condition is given in terms of linear matrix inequalities lmis which can be solved employing an lmis solver this novel approach seems to be an efficient tool to solve the problem of observer synthesis for a class of lipschitz systems of small dimensions

fe meshfree quad4 element for free vibration analysis the fe lspim quad4 element which was recently introduced for the static analysis uses new shape functions that combine the meshfree and finite element shape functions so as to synergize the individual strengths of meshfree and finite element methods as a result the element inherits the completeness properties of meshfree shape functions and the compatibility properties of finite element shape functions in this paper the element is extended to free vibration analysis of two dimensional solids typical benchmark problems are solved to test the efficacy of the element the results show that the element gives more accurate solution than the peer elements particularly under distorted mesh

moving particle finite element method with superconvergence nodal integration formulation and applications abstract a new approach of moving particle finite element method has been developed which is capable to gain a global superconvergence through solving particle kernel function to satisfy high order consistencies the nodal based moving particle finite element method inconjunction with the proposed superconvergence approach provides an optimized combination in numerical accuracy and computation efficiency the three dimensional engineering scale simulations demonstrate that this scheme is robust and capable to handle high speed penetration and dynamic crack propagation with intersonic and supersonic speeds

brief paper explicit construction of a barabanov norm for a class of positive planar discrete time linear switched systems we consider the stability under arbitrary switching of a discrete time linear switched system a powerful approach for addressing this problem is based on studying the most unstable switching law musl if the solution of the switched system corresponding to the musl converges to the origin then the switched system is stable for any switching law the musl can be characterized using optimal control techniques this variational approach leads to a hamilton jacobi bellman equation describing the behavior of the switched system under the musl the solution of this equation is sometimes referred to as a barabanov norm of the switched system although the barabanov norm was studied extensively it seems that there are few examples where it was actually computed in closed form in this paper we consider a special class of positive planar discrete time linear switched systems and provide a closed form expression for a corresponding barabanov norm and a musl the unit circle in this norm is a parallelogram

stability analysis of positive switched linear systems with delays this technical note addresses the stability problem of delayed positive switched linear systems whose subsystems are all positive both discrete time systems and continuous time systems are studied in our analysis the delays in systems can be unbounded under certain conditions several stability results are established by constructing a sequence of functions that are positive monotonically decreasing and convergent to zero as time tends to infinity additionally continuous for continuous time systems it turns out that these functions can serve as an upper bound of the systems trajectories starting from a particular region finally a numerical example is presented to illustrate the obtained results

symmetry respecting real space renormalization for the quantum ashkin teller model we use a simple real space renormalization group approach to investigate the critical behavior of the quantum ashkin teller model a one dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously this approach which is based on exploiting the on site symmetry of the model has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse field ising model our investigation explores this approach in more generality in a model in which the critical behavior has a richer structure but which reduces to the simpler ising case at a special point we demonstrate that the correlation length critical exponent as predicted from this real space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality near the ising special point the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods although the accuracy decreases away from the decoupled ising model point

application of radial basis functions to linear and nonlinear structural analysis problems the basic characteristic of the techniques generally known as meshless methods is the attempt to reduce or even to eliminate the need for a discretization at least not in the way normally associated with traditional finite element techniques in the context of numerical solutions for boundary and or initial value problems the interest in meshless methods is relatively new and this is why despite the existence of various applications of meshless techniques to several problems of mechanics as well as to other fields these techniques are still relatively unknown to engineers furthermore and compared to traditional finite elements it may be difficult to understand the physical meaning of the variables involved in the formulations as an attempt to clarify some aspects of the meshless techniques and simultaneously to highlight the ease of use and the ease of implementation of the algorithms applications are made in this work to structural analysis problems the technique used here consists of the definition of a global approximation for a given variable of interest in this case components of the displacement field by means of a superposition of a set of conveniently placed in the domain and on the boundary radial basis functions rbfs in this work various types of one dimensional problems are analyzed ranging from the static linear elastic case free vibration and linear stability analysis for a beam on elastic foundation to physically nonlinear damage models problems to further complement the range of problems analysed the static analysis of a plate on elastic foundation was also addressed several error measures are used to numerically establish the performance of both symmetric and nonsymmetric approaches for several global rbfs the results obtained show that rbf collocation leads to good approximations and very high convergence rates

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

nice reachability for planar bilinear control systems with applications to planar linear switched systems corrected we consider planar bilinear control systems with measurable controls we show that any point in the reachable set can be reached by a ldquonicerdquo control specifically a control that is a concatenation of a bang arc with either 1 a bang bang control that is periodic after the third switch or 2 a piecewise constant control with no more than two discontinuities under the additional assumption that the bilinear system is positive or invariant for any proper cone we show that the reachable set is spanned by a concatenation of a bang arc with either 1 a bang bang control with no more than two discontinuities or 2 a piecewise constant control with no more than two discontinuities in particular any point in the reachable set can be reached using a piecewise constant control with no more than three discontinuities several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result we demonstrate this with an example

a fictitious domain method using equilibrated basis functions for harmonic and bi harmonic problems in physics abstract in this paper we present a new meshless method to solve well known problems in physics and engineering with either constant or variable material properties in 2d space harmonic and bi harmonic problems are considered in this paper the method constructs a set of basis functions called equilibrated basis functions eqbfs through a weighted residual integration over a fictitious domain embedding the main one the bases can satisfy the governing partial differential equations approximately chebyshev polynomials of the first kind are employed to construct the eqbfs and exponential functions are used as the weights in the integrals the parameters of the solution are arranged so that all the integrals can be decomposed into much simpler 1d ones over a normalized intervals this reduces the computational efforts significantly either the eqbfs or the results of the integration process may be stored for further use the validity of the results is examined through an extended patch test a set of physical sample problems with variable non variable material properties as the potential flow over a cylinder steady state heat conduction problems in an anisotropic inhomogeneous functionally graded material potential and stokes flow through a channel of finite width obstructed by periodic cylinders and the bending of thin elastic plates having constant or variable thickness are solved to demonstrate the capabilities of the method as a preliminary study we show that the method may effectively be used in a domain decomposition approach

modelling three dimensional piece wise homogeneous domains using the α shape based natural element method in this paper the application of the natural element method nem to the numerical analysis of two and three dimensional piece wise homogeneous domains is presented the nem differs from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries the shape based extension of this method nem generalizes this behaviour to non convex domains enables us to construct models entirely in terms of the initial cloud of points and allows us to simulate material discontinuities in a straightforward manner in the following sections simple and effective algorithms are presented for the construction of shapes in domains composed of various materials examples are presented in two and three dimensional cases in the context of linear elastostatics showing good performance even with the simple numerical quadrature used copyright 2002 john wiley sons ltd

stability analysis of singularly perturbed switched linear systems this note is concerned with the stability of planar linear singularly perturbed switched systems we propose a characterization of the stability properties of such multiple time scale switched systems as the perturbation parameter goes to zero we also study transitions as this parameter varies and we restrict their number and nature finally we compare the results obtained in this way with the tikhonov type results for differential inclusions available in the literature

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

coupling three field formulation and meshless mixed galerkin methods using radial basis functions in this work we solve the elliptic partial differential equation by coupling the meshless mixed galerkin approximation using radial basis function with the three field domain decomposition method the formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

least squares collocation meshless method a finite point method least squares collocation meshless method is proposed except for the collocation points which are used to construct the trial functions a number of auxiliary points are also adopted unlike the direct collocation method the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least squares sense the moving least squares interpolant is used to construct the trial functions the computational effort required for the present method is in the same order as that required for the direct collocation while the present method improves the accuracy of solution significantly the proposed method does not require any mesh so that it is a truly meshless method three numerical examples are studied in detail which show that the proposed method possesses high accuracy with low computational effort copyright 2001 john wiley sons ltd

regular synthesis for time optimal control of single input real analytic systems in the plane for arbitrary single input real analytic systems in the plane in which the control enters linearly we prove the existence of a regular synthesis for the optimal control problem in which it is desired to minimize the integral of a strictly positive real analytic lagrangian that does not depend on the control variable the analysis proceeds by applying our previous results on nondegenerate mathcal c infty systems as well as those on arbitrary real analytic ones to study the local structure of the time optimal trajectories the structure of the optimal trajectories for our problem is derived by reparametrization of time the existence of a synthesis is then proved by using subanalytic set theory

applications of point interpolation method for spatial general shells structures the meshfree point interpolation method pim based on polynomial function is presented for the static analysis of spatial general shell structures the formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible shells based on the cosserat surface the pim technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property hence the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method an improved matrix triangularization algorithm mta is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis it is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non conforming pim npim when the energy principles are used to formulate pim to obtain compatible shape functions the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell based nodal selection is utilized which lead to conforming pim cpim both npim and cpim are evaluated in the paper several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the npim and cpim the phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy the convergences and performances are investigated for both conforming and non conforming pims it is also shown that the npim and cpim with the improved mta are very easy to implement and very efficient in constructing shape functions in comparison with the element free galerkin method

nodal integration of the element free galerkin method abstract spatial integration of the element free galerkin efg method is achieved by evaluating the integrals of the weak form only at the nodes in previous efg formulations a grid of cells was used to perform gaussian quadrature over the domain the absence of a cell structure for nodal integration results in a completely meshless method similar in simplicity to particle methods such as smooth particle hydrodynamics sph it is shown that nodal integration like sph suffers from spurious singular modes this spatial instability results from underintegration of the weak form and it is treated by the addition to the potential energy functional of a stabilization term which contains the square of the residual of the equilibrium equation example problems illustrate the effect of the stabilization and provide the basis for convergence studies

phase diagram and critical properties of the 1 1 dimensional ashkin teller model the 1 1 dimensional ashkin teller model is studied by the renormalisation group method and by the finite lattice extrapolation technique the possible phases and their boundaries in an extended space of couplings are determined from the degeneracy structure of the low lying levels in the thermodynamic limit the critical behaviour is investigated for ferromagnetic couplings using increasing block sizes in the renormalisation transformation the line of fixed points and its bifurcation at the potts fixed point is studied

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

meshless local petrov galerkin method for two dimensional nonlinear water wave problems in this paper the meshless local petrov galerkin mlpg method is extended to dealing with nonlinear water wave problems the formulation is based on general fluid governing equations and a time marching procedure at each time step the boundary value problem for the pressure is solved using the mlpg method and the velocity and position of nodes are updated by numerical integration the newly extended method is applied to simulating water waves generated by a wave maker and good agreement with analytical solutions and finite element results is presented

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

a simplification of the agrachev gamkrelidze second order variation for bang bang controls abstract we consider an expression for the second order variation sov of bang bang controls derived by agrachev and gamkrelidze the sov plays an important role in both necessary and sufficient second order optimality conditions for bang bang controls these conditions are stronger than the one provided by the first order pontryagin maximum principle pmp for a bang bang control with k switching points the sov contains k k 1 2 lie algebraic terms we derive a simplification of the sov by relating k of these terms to the derivative of the switching function defined in the pmp evaluated at the switching points we prove that this simplification can be used to reduce the computational burden associated with applying the sov to analyze optimal controls we demonstrate this by using the simplified expression for the sov to show that the chattering control in fuller s problem satisfies a second order sufficient condition for optimality

a meshless multilayer model for a coastal system by radial basis functions abstract a multilayer computational model for simulating three dimensional tidal flows in coastal waters is presented in this paper a truly meshless numerical scheme based on radial basis functions rbfs is employed to obtain an accurate approximation to the solution of the model for computational efficiency in solving large scale problems a noniterative domain decomposition method is combined with the use of the rbfs scheme to smooth the numerical simulation of the advection across each subdomain the commonly used upstream technique is also incorporated finally for numerical verification the proposed multilayer model is successfully used to obtain a stable and convergent simulation of the water flows in the pearl river estuary of the south china sea the numerical approximations exhibit good agreement with the observed tidal and current data

generating functions of switched linear systems analysis computation and stability applications in this paper a unified framework is proposed to study the exponential stability of discrete time switched linear systems and more generally the exponential growth rates of their trajectories under three types of switching rules arbitrary switching optimal switching and random switching it is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong the weak and the mean generating functions respectively in particular necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence various properties of the generating functions are established and their relations are discussed algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

local radial point interpolation mlrpi method for solving time fractional diffusion wave equation with damping the purpose of the current investigation is to determine numerical solution of time fractional diffusion wave equation with damping for caputo s fractional derivative of order 1 2 a meshless local radial point interpolation mlrpi scheme based on galerkin weak form is analyzed the reason of choosing mlrpi approach is that it does not require any background integrations cells instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape the unconditional stability and convergence with order o 6 2 are proved where is time stepping also several numerical experiments are illustrated to verify theoretical analysis

element free method for static and free vibration analysis of spatial thin shell structures the implementation of the element free galerkin method efg for spatial thin shell structures is presented in this paper both static deformation and free vibration analyses are considered the formulation of the discrete system equations starts from the governing equations of stress resultant geometrically exact theory of shear flexible shells moving least squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry discrete system equations are obtained by incorporating these interpolations into the galerkin weak form the formulation is verified through numerical examples of static stress analysis and frequency analysis of spatial thin shell structures for static load analysis essential boundary conditions are enforced through penalty method and lagrange multipliers while boundary conditions for frequency analysis are imposed through a weak form using orthogonal transformation techniques the efg results compare favorably with closed form solutions and that of finite element analyses

free mesh radial basis function collocation approach for the numerical solution of system of multi ion electrolytes the main objective of this work is to show the versatility of an innovative mesh free numerical scheme which allows the solution of the coupled transport equations governing the evolution of a system of multi ion electrolytes by mean of the use of radial basis functions interpolation and a nesting approach the nesting approach is used in order to capture the detail behaviour of the solution near a solid wall i e at the diffusion reaction layer as a numerical example the problem of silver deposition on a rotating disk is analysed the versatility of the proposed numerical scheme is proved by solving the proposed electrochemical phenomena imposing three different kinds of boundary conditions at the solid wall dirichlet neumann and robin the obtained numerical results are compared with simplified analytical approximation of the corresponding problems the effect of the ligand concentration on the others species is considered and a comparison between the obtained concentration profiles for the complex ags2o and ag s2o3 when the concentration of the ligand s2o takes different values is shown copyright 2005 john wiley sons ltd

on the stability of positive linear switched systems under arbitrary switching laws we consider n dimensional positive linear switched systems a necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is hurwitz several researchers conjectured that for positive linear switched systems this condition is also sufficient recently gurvits shorten and mason showed that this conjecture is true for the case n 2 but is not true in general their results imply that there exists some minimal integer np such that the conjecture is true for all n np but is not true for n np we show that np 3

a local search algorithm for natural neighbours in the natural element method a local basis algorithm for searching natural neighbours in natural element method nem is presented for solving the elasticity problems in this paper comparison with the global sweep algorithm used in natural element method or natural neighbour method nnm for searching natural neighbours the proposed algorithm is more expedient and convenient in the constructions and computation of natural neighbour interpolations in the proposed nem based on local search the laplace non sibson interpolations are constructed with respect to the natural neighbour nodes of the given point which have been locally defined the shape functions from the laplace approximations have the delta function property and the laplace interpolants are strictly linear between adjacent nodes which facilitate imposition of essential boundary conditions and treatment of material discontinuity with ease as it is in the conventional finite element method the laplace interpolants derived from the local algorithm and the global algorithm in nem are identical because of the uniqueness of the voronoi diagram numerical results and convergence studies also show that the present nem based on local search algorithm possesses the same accuracy and rate of convergence as they are in previous nem

meshless analysis of timoshenko beams based on a locking free formulation and variational approaches abstract a meshless method is developed based on subdomain variational formulations and a local petrov galerkin approximation along with the locking free formulation for the analysis of bending of a thick beam the local point interpolation method is employed to construct both trial and test functions the present method is a truly meshless method based only on a number of randomly located nodes no global background integration mesh is needed no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated problems of thick and thin beams under various loading and boundary conditions are analysed by the proposed method and the numerical results are compared with analytical solutions the contact problem for beam by means of subdomain variational inequalities and the meshless method has also been investigated

control systems which generate decomposable lie algebras let x y be real analytic vector fields on an n manifold m ad x y x y denote the lie product inductively ad k 1 x y x ad k x y and 1 ad v x y v 0 the attainable set at time t denoted download full size image t for the control system 1 x x x u t y x x 0 p u t 1 is contained in the integral manifold through p of the lie algebra l 1 generated by 1 l 1 is said to be decomposable at p if essentially when dim l 1 p n the solution of 1 can be written as exp tx exp f 1 t u v 1 exp f n t u v n p with v 1 v n l 1 this is true for example at any p if l 1 is nilpotent the f i t u are shown to satisfy a system on n of the form 2 x i u t g i t x 1 x i 1 x i 0 0 i 1 n where if l 1 is nilpotent each g i is a polynomial in x 1 x i 1 in this case reachability properties of 2 for controls being countably additive measures impluses reduce to the study of algebraic equations homogeneity allows these to be considered on projective space n giving local results by bezout s theorem similar results hold for controls in the unit ball of krener s results on approximating systems of the form 1 by systems which generate nilpotent lie algebras can then be used to remove the condition that l 1 be nilpotent the method applies to show that if m denotes the set of all products of k elements of 1 with k m and dim span m 1 p dim span m for all odd m then exp tx p int download full size image t for all t 0

third order nilpotency nice reachability and asymptotic stability we consider an affine control system whose vector fields span a third order nilpotent lie algebra we show that the reachable set at time t using measurable controls is equivalent to the reachable set at time t using piecewise constant controls with no more than four switches the bound on the number of switches is uniform over any final time t as a corollary we derive a new sufficient condition for stability of nonlinear switched systems under arbitrary switching this provides a partial solution to an open problem posed in d liberzon lie algebras and stability of switched nonlinear systems in v blondel a megretski eds unsolved problems in mathematical systems and control theory princeton univ press 2004 pp 203 207

on the stability of switched positive linear systems it was recently conjectured that the hurwitz stability of the convex hull of a set of metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching in this note we show that 1 this conjecture is true for systems constructed from a pair of second order metzler matrices 2 the conjecture is true for systems constructed from an arbitrary finite number of second order metzler matrices and 3 the conjecture is in general false for higher order systems the implications of our results both for the design of switched positive linear systems and for research directions that arise as a result of our work are discussed toward the end of the note