full analytical sensitivities in nurbs based isogeometric shape optimization abstract non uniform rational b spline nurbs has been widely used as an effective shape parameterization technique for structural optimization due to its compact and powerful shape representation capability and its popularity among cad systems the advent of nurbs based isogeometric analysis has made it even more advantageous to use nurbs in shape optimization since it can potentially avoid the inaccuracy and labor tediousness in geometric model conversion from the design model to the analysis model although both positions and weights of nurbs control points affect the shape until very recently usually only control point positions are used as design variables in shape optimization thus restricting the design space and limiting the shape representation flexibility this paper presents an approach for analytically computing the full sensitivities of both the positions and weights of nurbs control points in structural shape optimization such analytical formulation allows accurate calculation of sensitivity and has been successfully used in gradient based shape optimization the analytical sensitivity for both positions and weights of nurbs control points is especially beneficial for recovering optimal shapes that are conical e g ellipses and circles in 2d cylinders ellipsoids and spheres in 3d that are otherwise not possible without the weights as design variables

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

reliable guaranteed variance filtering against sensor failures this paper presents a solution to a reliable filtering problem with error variance specifications for both continuous and discrete time systems the filtering error variance in the sensor failure cases is guaranteed to be less than a given upper bound while the performance in the nominal case is optimized a convergent iterative algorithm based on linear matrix inequality lmi is given to obtain the solution the algorithm solves the problem without introducing additional conservativeness and it is shown to get better performance and be less conservative compared with traditional lmi approaches a numerical example is given to show the advantages of our approach over existing techniques

simultaneous stabilization via static output feedback and state feedback in this paper the simultaneous stabilization problem is considered using the matrix inequality approach some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi input multi output mimo plants via static output feedback and state feedback are obtained in the form of coupled algebraic riccati inequalities it is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term a heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities the effectiveness of the approach is illustrated by numerical examples

a new necessary and sufficient condition for static output feedback stabilizability and comments on stabilization via static output feedback in this paper a counterexample of the above mentioned paper by trofino neto et al ibid vol 38 1993 is reported it is pointed out that one of the conditions for a linear system to be stabilizable via static output feedback is not correct a modified necessary and sufficient condition for this problem is also presented

optimal simultaneous stabilization of linear single input systems via linear state feedback control simultaneous stabilization of a collection of linear time invariant systems is considered the aim is to develop a practical method for the design of a single feedback controller such that all the systems involved are stabilized with good transient responses hurwitz s necessary and sufficient conditions are used as the required set of constraints for simultaneous stability for transient behaviour we introduce the usual quadratic objective function as performance index for each system their sum is the objective function for the collection of systems and the problem is to minimize it by choosing a feedback gain vector subject to boundedness and the hurwitz stability constraints a computational technique is proposed for solving this problem the results obtained give good transient behaviour for illustration two numerical examples are solved

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

technical communique design of static output feedback controller for uncertain systems this paper considers the problem of designing a single static output feedback stabilizing controller for a finite set of linear systems for this purpose a set of square equal number of inputs and outputs minimum phase systems is considered using the notions of quadratic stabilizability the existence of output feedback controller is derived in terms of the solvability of a set of matrix inequalities then the existence of the solution of such inequalities are derived for special class of systems it is proved that a set of partially commutative or partially normal systems are stabilizable by a single static output feedback controller these classes of systems are shown to be different from the well known matched uncertain systems and considered to be new classes of systems an algorithm is also presented to compute the controller gain

a theorem on global stabilization of nonlinear systems by linear feedback abstract in this paper we investigate the global stabilizability problem for a wide class of single input nonlinear systems whose the linearization at the equilirrium is controllable we show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium the proof of our main theorem is based on some ideas from a previous paper we use the theorem to recover a recent result of gauthier et al concerning the observer design problem

algorithms of maximum likelihood data clustering with applications abstract we address the problem of data clustering by introducing an unsupervised parameter free approach based on maximum likelihood principle starting from the observation that data sets belonging to the same cluster share a common information we construct an expression for the likelihood of any possible cluster structure the likelihood in turn depends only on the pearson s coefficient of the data we discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations compared to standard clustering methods our approach has the advantages that i it is parameter free ii the number of clusters need not be fixed in advance and iii the interpretation of the results is transparent in order to test our approach and compare it with standard clustering algorithms we analyze two very different data sets time series of financial market returns and gene expression data we find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability

sufficient lmi conditions for output feedback control problems the authors present linear matrix inequality lmi conditions for output feedback control problems the results are based on sufficient conditions because they are dependent on the particular state space representation used for describing the system nevertheless the conditions are not sensitive to a certain class of state space transformations and if the control problem is feasible then there exists some state space transformation leading the conditions to be necessary and sufficient for the problem the authors approach can be used for designing decentralized controllers and is easily extended to h sub 2 h sub spl infin and mixed h sub 2 h sub spl infin problems via standard lmi techniques the continuous and discrete time cases are considered and numerical examples are given to illustrate the results

a revisit to inverse optimality of linear systems in this article we revisit the problem of inverse optimality for linear systems by applying certain explicit formulae for coprime matrix fraction descriptions cmfd of linear systems we propose a necessary and sufficient condition for a given stable state feedback law to be optimal for some quadratic performance index compared to existing results in the literature the proposed condition is simpler to check and interpret moreover it reduces the redundancy in the solutions of the associated algebraic riccati equation are as a direct application of the proposed results we consider the problem of inverse optimality of observer based state feedback to be specific for the case where the state is not fully known we consider the inverse optimality problem of an observer based state feedback for the closed loop system augmented by an observer more precisely it is shown that the observer based state feedback is inverse optimal for the closed loop system with some general forms of cost functions on

optimization of static output feedback using substitutive lmi formulation this note proposes a new design tool for optimizing static output feedback using a linear matrix inequality lmi formula called substitutive lmi a matrix inequality derived from static output feedback is not usually linear adding a positive definite term including auxiliary variables the matrix inequality is transformed into an lmi with respect to the positive definite matrix and the static output feedback gain an iterative calculation algorithm is given to solve the substitutive lmi in this note designs of the static output feedback gain are shown in the frame of h sub spl infin and h sub 2 syntheses a numerical example is shown to demonstrate the effectiveness of the proposed technique

some new results on strong gamma_k gamma_ cl h_ infty stabilization the strong gammak gammacl hinfin stabilization problem is addressed in this paper based on the bounded real lemma an improved sufficient condition on strong hinfin stabilization as well as its dual form is derived which extends the are constraint in the former results into an inequality constraint two path following algorithms are proposed to solve the associated optimization problems with bmi constraints which lead to full order controllers a numerical example is presented to demonstrate the effectiveness of the result

alternating convex projection methods for covariance control design the problem of designing a static state feedback or full order dynamic controller is formulated as a problem of designing an appropriate plant state covariance matrix we show that closed loop stability and multiple output norm constraints imply that the plant state covariance matrix lies at the intersection of some specified closed convex sets in the space of symmetric matrices we address the covariance feasibility problem to determine the existence and compute a covariance matrix to satisfy assignability and output norm performance constraints we address the covariance optimization problem to construct an assignable covariance matrix which satisfies output performance constraints and is as close as possible to a given desired covariance we also treat inconsistent constraints where we look for an assignable covariance matrix which best approximates desired but non achievable output performance objectives we call this the infeasible covariance optimization problem all these problems are of a conve

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

linear quadratic suboptimal control with static output feedback abstract this paper considers the design of a stabilizing static output feedback gain which keeps linear quadratic lq performance index less than a specified number we call this an lq suboptimal controller existence of such a controller is shown to be equivalent to the existence of a positive definite matrix p such that p satisfies two linear matrix inequalities lmis while p 1 satisfies another lmi all lq suboptimal controllers are explicitly parametrized by the freedom in the choice of the positive definite matrix p satisfying the lmis and an arbitrary positive scalar and an arbitrary matrix of fixed dimension with a norm bound a modified version of the min max algorithm is given to find a positive definite solution p to the lmis

simultaneous stabilization using stable system inversion abstract this paper investigates the use of stable system inversion to design controllers for the simultaneous stabilization of multi input multi output systems a parametrization of all simultaneously stabilizing controllers for systems admitting a stable inverse is developed the controller is shown to have the structure of a generalized observer for strictly proper systems an intermediate step of the design requires solving a sequence of strong stabilization subproblems for systems with components having identical stable minimum phase transfer functions the design requires only a single model of the component in the controller in systems where a stable inverse fails to exist an interpolation scheme is proposed to develop a stabilizing controller

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

static output feedback and guaranteed cost control of a class of discrete time nonlinear systems with partial state measurements abstract in this paper both the static output feedback issue and the observer based control of a class of discrete time nonlinear systems are considered thanks to a newly developed linearization lemma it is shown that the solution of the discrete time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint an illustrative example is provided to show the usefulness of the proposed control designs

stabilization of discrete time linear systems by static output feedback this note proposes a systematic approach for the static output feedback control design for discrete time linear systems it is shown that if the open loop system satisfies some particular structural conditions a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the stronger relies on a minimum phase argument square and nonsquare systems are considered

algorithm for simultaneous stabilization of single input systems via dynamic feedback using a sufficient algebraic stability criterion for polynomials an algorithm is deduced for the design of dynamic feedback which simultaneously stabilizes a set of single input systems the application of this algorithm to the stabilization problem of an aircraft is also presented

static output feedback controllers stability and convexity the main objective of this paper is to solve the following stabilizing output feedback control problem given matrices a b sub 2 c sub 2 with appropriate dimensions find if one exists a static output feedback gain l such that the closed loop matrix a b sub 2 lc sub 2 is asymptotically stable it is known that the existence of l is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs hence this paper provides a new sufficient but not necessary condition for the solvability of the above stabilizing output feedback control problem as a natural extension we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index some examples borrowed from the literature are solved to illustrate the theoretical results

a control scheme for a class of discrete nonlinear stochastic systems a control scheme is presented for effective stabilization of discrete time nonlinear stochastic systems where the nonlinearity involves a zero mean independent random sequence the control is of a constant feedback type and makes use of finite time solutions of a riccati like matrix difference equation stability results are both in terms of mean square and almost sure stochastic stability moreover a matrix inequality is given to check the existence of weighting matrices which would result in a stable regulator problem

authors reply to comments on on the discrete time normal form kotta 2000 commented on the above paper by califano et al 1998 kotta made two main criticisms in this paper the original authors reply to them

isogeometric analysis with trimming technique for problems of arbitrary complex topology trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to cad files created by using nurbs in the present work it is shown that any complex multiply connected nurbs domain can be described by using trimming curves only isogeometric analysis for linear elasticity problems of complex topology described in this way is presented for fully communicative interaction between cad and cae a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the iges files exported from cad system for isogeometric analysis schemes for imposing essential and traction boundary conditions on trimming curves are presented it has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated with the examples of complex topology that could be described by employing trimming curves only effectiveness and robustness of present method are demonstrated

bootstrap validation of links of a minimum spanning tree abstract we describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables we show that two different bootstrap procedures provide partly distinct information that can be informative about the investigated complex system we investigate two case studies by considering daily returns of two portfolios of stocks traded in the us equity markets in different time periods the first method performs a row bootstrap whereas the second method performs a pair bootstrap to obtain a bootstrap replica of each correlation coefficient we show that the parallel use of the two methods can highlight details about the stability of links selected by the minimum spanning tree associated with the correlation matrix of stock portfolios that can be missed by applying only a single bootstrap methods

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

static output feedback stabilisation with h performance for a class of plants in this paper the problem of static output feedback control of a linear system is considered the existence of a static output feedback control law is given in terms of the solvability of two coupled lyapunov inequalities which result in a non linear optimisation problem however using state coordinate and congruence transformations and by imposing a block diagonal structure on the lyapunov matrix we will see that the determination of a static output feedback gain reduces for a specific class of plants to finding the solution of a system of linear matrix inequalities the class of plants considered is those which are minimum phase with a full row rank markov parameter the method is extended to incorporate h performance objectives this results in a sub optimal static h control law found by non iterative means the simplicity of the method is demonstrated by a numerical example

stabilization of nonlinear discrete time systems using state detection some recent results concerning stabilization of continuous time systems using state detection are extended to the case of discrete time nonlinear systems it is shown that if a discrete time locally detectable system can be stabilized by a state feedback law then it can also be stabilized by a feedback law that depends on the output of a weak detector

a goal oriented error estimator for the analysis of simplified designs abstract simplifying an engineering design by removing geometric details can significantly reduce the complexity of downstream tasks of mesh generation and field solution computation however lack of a proper analysis and estimates of the errors induced by design simplification remains a bottleneck in seamless cad cae integration to address this issue this paper develops a general framework for providing a posteriori estimates of goal oriented engineering analysis error caused by removing a negative feature or void where material is absent from an engineering design our approach is built upon the idea of representing it as a modeling error defined in the same geometry which is then estimated using the dual weighted residual method the derived error estimator still involves an uncomputable term involving dual errors which is removed by further simplification into a term on the feature s boundary via an exterior solution in linear cases or problem specific approaches in nonlinear cases utilizing classical theories of differential operators we illustrate our approach via a semilinear second order elliptic equation and explicit error estimators are also derived for the classical poisson equation and linear elasticity results of numerical tests are shown and comparisons made with results obtained with related approaches

brief paper an lmi approach to h index and mixed h h fault detection observer design using the newly developed worst case fault sensitivity measure the index and the well known worst case robustness measure the norm this paper addresses the problem of index fault detection observer design and multiobjective fault detection observer design problems necessary and sufficient conditions for the existence of such a fault detection observer are given in terms of matrix inequalities both infinite frequency range case 0 and finite frequency range case 0 with overbar are considered iterative linear matrix inequality ilmi algorithms are given to obtain the solutions the effectiveness of the proposed approaches is shown by numerical examples

second order topological sensitivity analysis abstract the topological derivative provides the sensitivity of a given cost function with respect to the insertion of a hole at an arbitrary point of the domain classically this derivative comes from the second term of the topological asymptotic expansion dealing only with infinitesimal holes however for practical applications we need to insert holes of finite size therefore we consider one more term in the expansion which is defined as the second order topological derivative in order to present these ideas in this work we apply the topological shape sensitivity method as a systematic approach to calculate first as well as second order topological derivative for the poisson s equations taking the total potential energy as cost function and the state equation as constraint furthermore we also study the effects of different boundary conditions on the hole neumann and dirichlet both homogeneous finally we present some numerical experiments showing the influence of the second order topological derivative in the topological asymptotic expansion which has two main features it allows us to deal with hole of finite size and provides a better descent direction in optimization process

simultaneous quadratic stabilization for discrete time nonlinear systems a constructive method is developed for designing simultaneously quadratically stabilizing state feedback controllers for a collection of single input discrete time nonlinear systems in the context of quadratic control lyapunov functions a necessary and sufficient condition for the existence of simultaneously quadratically stabilizing state feedback laws is derived an explicit formula for constructing continuous simultaneously stabilizing controllers is presented the obtained results are verified by a numerical example

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

topological sensitivity analysis for three dimensional linear elasticity problem in this work we use the topological shape sensitivity method to obtain the topological derivative for three dimensional linear elasticity problems adopting the total potential energy as cost function and the equilibrium equation as constraint this method based on classical shape sensitivity analysis leads to a systematic procedure to calculate the topological derivative in particular firstly we present the mechanical model later we perform the shape derivative of the corresponding cost function and finally we calculate the final expression for the topological derivative using the topological shape sensitivity method and results from classical asymptotic analysis around spherical cavities in order to point out the applicability of the topological derivative in the context of topology optimization problems we use this information as a descent direction to solve a three dimensional topology design problem furthermore through this example we also show that the topological derivative together with an appropriate mesh refinement strategy are able to capture high quality shapes even using a very simple topology algorithm

comments on stabilization via static output feedback in the above paper trofino neto and kucera 1993 the proof given for theorem 3 1 is inconsistent in this note a modified proof is suggested

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

identification of clusters of companies in stock indices via potts super paramagnetic transitions the clustering of companies within a specic stock market index is studied by means of super paramagnetic transitions of an appropriate q state potts model where the spins correspond to companies and the interactions are functions of the correlation coecients determined from the time dependence of the companies individual stock prices the method is a generalization of the clustering algorithm by domany et al to the case of anti ferromagnetic interactions corresponding to anti correlations for the dow jones industrial average where no anti correlations were observed in the investigated time period the previous results obtained by dierent tools were well reproduced for the standard poor s 500 where anti correlations occur repulsion between stocks modify the cluster structure c 2000 elsevier science b v all rights reserved stock market indices like the dow jones dj or standard poor s 500 s p 500 are used as indicators of the status of the markets they are averaged values of a dierent number of selected companies indicative of the economy of a given market it is of both theoretical and practical importance to analyze how individual contributions to the average behave the customary approach in the nancial literature focuses on the investigation of the properties of the covariance matrix here we take a dierent approach aiming to identify the presence of a hierarchical structure inside the set of stocks simultaneously traded in a market the identication of the hierarchy of clusters is of central importance both from the point of view of understanding the dynamics of

brief robust stabilization and guaranteed cost control for discrete time linear systems by static output feedback this paper proposes a systematic approach for the static output feedback control design for discrete time uncertain linear systems it is shown that if the open loop system satisfies some particular structural conditions and the uncertainty has a specific structure a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the strongest one relies on a minimum phase argument square and nonsquare systems are considered the performance problem through a quadratic criterion is also discussed guaranteed cost control

stabilization via static output feedback necessary and sufficient conditions for the existence of a stabilizing static output feedback gain matrix are presented it is shown that any such gain matrix is the solution of some linear quadratic control problem where the cost functional has a suitable cross term

an improved ilmi method for static output feedback control with application to multivariable pid control an improved iterative linear matrix inequality ilmi algorithm for static output feedback sof stabilization problem without introducing any additional variables is proposed in this note the proposed ilmi algorithm is also extended to solve the sof hinfin controller design problem they are applied to the multivariable pid controllers numerical examples show that the proposed algorithms yield better results and faster convergence than the existing ones

brief paper simultaneous lq control of a set of lti systems using constrained generalized sampled data hold functions in this paper sampled data control of a set of continuous time lti systems is considered it is assumed that a predefined guaranteed continuous time quadratic cost function which is in fact the sum of the performance indices for all systems is given the main objective here is to design a decentralized periodic output feedback controller with a prespecified form e g polynomial piecewise constant exponential etc which minimizes the above mentioned guaranteed cost function this problem is first formulated as a set of matrix inequalities and then by using a well known technique it is reformulated as a lmi problem the set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form rather than a general form moreover an algorithm is presented to solve the resultant lmi problem finally the efficiency of the proposed method is demonstrated in two numerical examples

robust observer based control of systems with state perturbations via lmi approach in this note the observer based control for a class of uncertain linear systems is considered exponential stabilizability for the systems is studied and the convergence rate of the system is estimated a linear matrix inequality lmi approach is used to design the observer based control the control and observer gains are given from lmi feasible solution a numerical example is given to illustrate our results

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

application of a multiplier method to uncertain lur e like systems abstract this paper investigates the conditions under which an abstract matrix multiplier method can be applied to determine guaranteeing cost controls for systems containing nonlinear uncertain elements via linear matrix inequalities lmis quadratically constrained uncertainties and nonlinearities are considered which comprehend the cases of norm bounded positive real and sector bounded uncertainties nonlinearities both the discrete time and the continuous time cases are discussed necessary and sufficient conditions are formulated in the case of unstructured uncertainty the conditions are sufficient in the structured case the cost guaranteeing controls can be determined by solving lmis numerical examples illustrate the effectiveness of the proposed method

simultaneous control of linear systems by state feedback in this paper a new method for finding a state feedback matrix in order to control simultaneously a collection of linear systems of the same size by using similarity operations is presented for stabilization of all the systems it is necessary that the eigenvalues of the closed loop systems lie inside a specified region in the left hand side of the complex plane this aim is achieved by solving linear and nonlinear parametric systems of equations using nonlinear programming the presented method is implemented in two examples and the results are verified in view of the norm of the state feedback matrix and stabilizability

a necessary and sufficient condition for output feedback stabilizability a necessary and sufficient condition for a linear system to be stabilizable via static output feedback is presented it makes an appeal to the linear quadratic regulator theory

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

output feedback decentralized stabilization ilmi approach in this paper the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach a necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time invariant large scale systems it is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality the extension of the result to h control is studied an iterative lmi algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain examples show the effectiveness of the algorithm

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

a convergent algorithm for computing stabilizing static output feedback gains we revisit the approach by cao et al that uses a fixed structure control law to find stabilizing static output feedback gains for linear time invariant systems by performing singular value decomposition on the output matrix together with similarity transformations we present a new stabilization method unlike their results that involve a difficult modified riccati equation whose solution is coupled with other two intermediate matrices that are difficult to find we obtain lyapunov equations we present a convergent algorithm to solve the new design equations for the gains we will show that our new approach like theirs is a dual optimal output feedback linear quadratic regulator theory numerical examples are given to illustrate the effectiveness of the algorithm and validate the new method

solid t spline construction from boundary representations for genus zero geometry abstract this paper describes a novel method to construct solid rational t splines for complex genus zero geometry from boundary surface triangulations we first build a parametric mapping between the triangulation and the boundary of the parametric domain a unit cube after that we adaptively subdivide the cube using an octree subdivision project the boundary nodes onto the input triangle mesh and at the same time relocate the interior nodes via mesh smoothing this process continues until the surface approximation error is less than a pre defined threshold t mesh is then obtained by pillowing the subdivision result one layer on the boundary and its quality is improved templates are implemented to handle extraordinary nodes and partial extraordinary nodes in order to get a gap free t mesh the obtained solid t spline is c 2 continuous except for the local region around each extraordinary node and partial extraordinary node the boundary surface of the solid t spline is c 2 continuous everywhere except for the local region around the eight nodes corresponding to the eight corners of the parametric cube finally a bezier extraction technique is used to facilitate t spline based isogeometric analysis the obtained bezier mesh is analysis suitable with no negative jacobians several examples are presented in this paper to show the robustness of the algorithm

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

boundaries of conditional quadratic forms a comment on stabilization via static output feedback motivated by the above paper trofino neto and kucera ibid vol 38 no 5 p 764 65 1993 this note considers the boundaries of a quadratic form with all possible constraints over a given subspace essential upper or lower bounds are presented provided they exist it mends a mild incompleteness in the proof of the main result

adaptive control of passifiable linear systems with quantized measurements and bounded disturbances we consider a linear uncertain system with an unknown bounded disturbance under a passification based adaptive controller with quantized measurements first we derive conditions ensuring ultimate boundedness of the system then we develop a switching procedure for an adaptive controller with a dynamic quantizer that ensures convergence to a smaller set the size of the limit set is defined by the disturbance bound finally we demonstrate applicability of the proposed controller to polytopic type uncertain systems and its efficiency by the example of a yaw angle control of a flying vehicle

simultaneous stabilization of linear single input systems by linear state feedback control a necessary and sufficient condition for the existence of a linear state feedback controller which will simultaneously stabilize a finite collection of single input linear systems is presented this condition can be checked numerically through the solution of a non linear programming problem presented here and can be used to determine whether or not a particular simultaneous stabilization problem has a solution if the stabilization problem has a solution the method provides a means of constructing a suitable controller the proposed method is very versatile it is a simple matter to limit the size of elements of the feedback gain vector and thus ensure that the control action is not excessive in addition for simultaneous stabilization problems which have a range of possible solutions the proposed method makes it possible to select one which yields good performance

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

output consensus for high order linear time invariant swarm systems output consensus analysis and design problems of high order linear time invariant swarm systems are investigated first an output consensus subspace and a complement output consensus subspace are introduced by output projection onto the two subspaces and the partial stability theory a necessary and sufficient condition for output consensus is presented and an explicit expression of the output consensus function which is jointly determined by the interaction topology and initial states of all agents is given especially it is shown that the output consensus function is completely determined by initial states of all agents if the interaction topology is balanced then an approach to determine gain matrices in consensus protocols of swarm systems is proposed which has less calculation complexity finally a numerical example is shown to demonstrate theoretical results

contact treatment in isogeometric analysis with nurbs abstract we study nurbs based isogeometric analysis of contact problems and compare with standard c 0 continuous lagrange finite elements a knot to surface kts algorithm is developed to treat the contact constraints with nurbs contact surface discretizations qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems quantitative studies based on the hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard kts approach the improved mortar based kts algorithm delivers robust and accurate results for nurbs discretizations based on numerical examples we conclude that nurbs based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over c 0 continuous finite elements

defeaturing a posteriori error analysis via feature sensitivity it is well known that small geometric features within a cad model can significantly impact the computational cost and often undermine the reliability of finite element analysis engineers therefore resort to defeaturing or detail removal wherein the offending features are suppressed prior to computational analysis however this results in a defeaturing induced analysis error in this paper we estimate this error in an a posteriori sense through the novel concept of feature sensitivity the latter determines the first order change in quantities of interest when an arbitrary cluster of small geometric features is deleted from a model a formal theory and a set of associated algorithms are provided to compute the feature sensitivity associated with a scalar elliptic partial differential equation the theory is supported through numerical experiments in 2 d involving both internal and boundary features copyright 2008 john wiley sons ltd

output consensus analysis and design for high order linear swarm systems partial stability method output consensus analysis and design problems for high order linear time invariant swarm systems with directed interaction topologies are investigated firstly as foundations of our approaches several conclusions about partial stability are given then two subspaces of the output space of swarm systems namely an output consensus subspace and a complement output consensus subspace are introduced based on output projection onto the two subspaces and partial stability necessary and or sufficient conditions for output consensus and limited control energy consensus are proposed respectively an explicit expression of the output consensus function is presented based on the different contributions of initial states of agents and protocols and an approach independent of the number of agents is shown to determine the gain matrices of output consensus protocols finally a numerical example is given to demonstrate the theoretical results

simultaneous stabilization for a collection of single input nonlinear systems this paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single input nonlinear systems the control lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time invariant simultaneously stabilizing state feedback controllers additionally a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented for any collection of second order and third order feedback linearizable systems in canonical form global simultaneous stabilization via a single state feedback controller is shown to be always possible two examples are included for illustration

the solution of a transcendental problem and its applications in simultaneous stabilization problems a complete solution for a special transcendental problem in system theory is given one of the interpretations of this transcendental problem is the following simultaneous stabilization problem under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane these conditions are completely general and therefore encompass unstable non minimum phase plants as well it is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane for two plants satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is provided and illustrated a computationally checkable necessary condition for simultaneous stabilization of three plants is also given

on a conservative concept for output static stabilizability analysis consequences and related problems this communication is concerned with the problem of stabilization via output static feedback of linear time invariant finite dimensional systems a new output static stabilization concept is introduced output static stabilization in the relaxed sense this conservative stabilization concept is the result of imposing an additional condition to a set of necessary and sufficient conditions for output static stabilization this paper is devoted to exhaustively study the introduced new stabilization concept i it is shown that for a particular class of plants the stabilization problem in the above sense can be cast as a convex programming problem ii a full characterization of the class of plants that are stabilizable in the above new sense is presented some of the important consequences of that study are as follows 1 the identification of a class of plants stabilizable via output static feedback for which stabilizing feedback matrices can be almost expressed in analytic closed form 2 it is

on the existence of linear optimal control with output feedback a necessary and sufficient condition is established for the existence of an output feedback u ky that is lq optimal with respect to some nonsingular quadratic cost a fact that entails robustness in the closed loop systems it is shown that if the system with equal number of inputs and outputs is strict minimum phase and has nonsingular high frequency gain then there exists a linear static output feedback that minimizes a certain quadratic cost functional the minimization of h infty norm of the closed loop system with output feedback is also discussed

input saturation and global stabilization of nonlinear systems via state and output feedback for multi input multi output nonlinear systems whose free dynamics are lyapunov stable the author shows how the problem of global stabilization via dynamic output feedback can be solved by using the technique of input saturation the power of this technique is also illustrated by solving the problem of global stabilization via bounded state feedback for affine nonlinear systems with stable unforced dynamics analogous results are established for discrete time nonlinear systems

a gradient flow approach to decentralized output feedback optimal control this paper visits the quadratic optimal control problem of decentralised control systems via static output feedback a gradient flow approach is introduced as a tool to compute the optimal output feedback gain several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost i e the objective cost is decreasing along this trajectory if the equilibrium points are isolated the convergence can be guaranteed a simulation example is given to illustrate the effectiveness of this approach

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

to stabilize a k real parameter affine family of plants it suffices to simultaneously stabilize 4 4 polynomials a controller stabilizes an entire family of plants with affine uncertainty if it simultaneously stabilizes a finite number of polynomials an upper bound for this number is 4k

data clustering and noise undressing of correlation matrices we discuss an approach to data clustering we find that maximum likelihood leads naturally to an hamiltonian of potts variables that depends on the correlation matrix and whose low temperature behavior describes the correlation structure of the data for random uncorrelated data sets no correlation structure emerges on the other hand for data sets with a built in cluster structure the method is able to detect and recover efficiently that structure finally we apply the method to financial time series where the low temperature behavior reveals a nontrivial clustering