stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

a unifying convergence analysis of second order methods for secular equations existing numerical methods of second order are considered for a so called secular equation we give a brief description of the most important of these methods and show that all of them can be interpreted as improvements of newton s method for an equivalent problem for which newton s method exhibits convergence from any point in a given interval this interpretation unifies the convergence analysis of these methods provides convergence proofs where they were lacking and furnishes ways to construct improved methods in addition we show that some of these methods are in fact equivalent a second secular equation is also briefly considered

adaptive fuzzy output feedback control for output constrained nonlinear systems in the presence of input saturation abstract in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states to address output constraint and input constraint a barrier lyapunov function and an auxiliary design system are employed respectively fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are bounded and the input and output constraints are circumvented simultaneously a numerical example is provided to illustrate the effectiveness of the proposed approach

on computing of arbitrary positive integer powers of odd order anti tridiagonal matrices with zeros in main skew diagonal and elements 1 1 1 1 1 1 1 1 in neighbouring diagonals in this paper we derive the general expression of the lth power email protected n for one type of anti tridiagonal matrices of odd order

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

improved h control of discrete time fuzzy systems a cone complementarity linearization approach in this paper new results are presented for h analysis and synthesis problems of discrete time takagi sugeno ts fuzzy systems by defining a multiple lyapunov function a new sufficient condition guaranteeing the h performance of the ts fuzzy systems is first derived which is expressed by a set of linear matrix inequalities lmis both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework based on this new condition for h performance the corresponding h controller design problem is then investigated different from the traditional quadratic framework the synthesis problem is solved by exploiting the cone complementarity linearization ccl method together with a sequential minimization problem subject to lmi constraints obtained for the existence of admissible controllers which can be readily solved by using standard numerical software

quadratically constrained least squares and quadratic problems we consider the following problem compute a vectorx such that ax b 2 min subject to the constraint x 2 a new approach to this problem based on gauss quadrature is given the method is especially well suited when the dimensions ofa are large and the matrix is sparse it is also possible to extend this technique to a constrained quadratic form for a symmetric matrixa we consider the minimization ofx t a x 2b t x subject to the constraint x 2 some numerical examples are given

a new matrix free algorithm for the large scale trust region subproblem we present a new method for the large scale trust region subproblem the method is matrix free in the sense that only matrix vector products are required we recast the trust region subproblem as a parameterized eigenvalue problem and compute an optimal value for the parameter we then find the solution of the trust region subproblem from the eigenvectors associated with two of the smallest eigenvalues of the parameterized eigenvalue problem corresponding to the optimal parameter the new algorithm uses a different interpolating scheme than existing methods and introduces a unified iteration that naturally includes the so called hard case we show that the new iteration is well defined and convergent at a superlinear rate we present computational results to illustrate convergence properties and robustness of the method

fast and stable qr eigenvalue algorithms for generalized companion matrices and secular equations we introduce a class of n n structured matrices which includes three well known classes of generalized companion matrices tridiagonal plus rank one matrices comrade matrices diagonal plus rank one matrices and arrowhead matrices relying on the structure properties of we show that if a then a rq where a qr is the qr decomposition of a this allows one to implement the qr iteration for computing the eigenvalues and the eigenvectors of any a with o n arithmetic operations per iteration and with o n memory storage this iteration applied to generalized companion matrices provides new o n2 flops algorithms for computing polynomial zeros and for solving the associated rational secular equations numerical experiments confirm the effectiveness and the robustness of our approach

control design for fuzzy systems based on relaxed nonquadratic stability and h_ infty performance conditions in this paper new approaches to hinfin controller design for a class of discrete time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis dependent lyapunov functions are used first two relaxed conditions of nonquadratic stability with h infin norm bound are presented for this class of systems the two relaxed conditions are shown to be useful in designing fuzzy control systems by introducing some additional instrumental matrix variables the two relaxed conditions are used to develop hinfin controllers in the control design the first relaxed condition has fewer inequality constraints but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables finally two examples are given to demonstrate the applicability of the proposed approach

stabilization for t s model based uncertain stochastic systems this paper considers the stabilization problem of a class of uncertain ito stochastic fuzzy systems driven by a multidimensional wiener process the uncertainty modeled in the systems is of the linear fractional type which includes the norm bounded uncertainty as a special case the objective is to design a state feedback fuzzy controller such that the closed loop system is robustly asymptotically stable under a stochastic setting by using a stochastic lyapunov approach sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique the derived stability conditions are then employed to design controllers which stabilize the uncertain ito stochastic fuzzy systems two simulation examples are given to illustrate the effectiveness of the approaches proposed

robust exponential stability of uncertain systems with time varying delays focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time varying delays the uncertainties are assumed to be continuous time varying nonlinear and norm bounded sufficient conditions for robust exponential stability are given for both single and multiple delays cases

convection patterns in large aspect ratio systems abstract a theory which should have widespread application is developed to treat the statics and slow dynamics of patterns of convective rolls encountered in large aspect ratio rayleigh benard boxes for case of presentation the theory is developed using model equations wavenumber selection the shape of patterns stability and the time dependence resulting from long wavelength instabilities are discussed the effects of adding the local mean drift important in low prandtl number situations are investigated our theory includes the notion of the busse stability balloon reduces near critical values of the stress parameter to the newell whitehead segel equations and contains the pomeau manneville phase equation it also gives a detailed description of the way in which the field amplitude which is slaved to the phase gradient away from threshold becomes an independent order parameter near the critical point

technical communique fuzzy h output feedback control of nonlinear systems under sampled measurements this paper studies the problem of designing an h fuzzy feedback control for a class of nonlinear systems described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are allowed to be unavailable we develop a technique for designing an h fuzzy feedback control that guarantees the l 2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value a design algorithm for constructing the h fuzzy feedback controller is given

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

on anti pentadiagonal persymmetric hankel matrices with perturbed corners in this paper we express the eigenvalues of real anti pentadiagonal persymmetric hankel matrices with perturbed corners as the zeros of explicit rational functions from these prescribed eigenvalues we give an orthogonal diagonalization for these matrices and a formula to compute its integer powers in particular an explicit expression not depending on any unknown parameter for the determinant and the inverse of complex anti pentadiagonal persymmetric hankel matrices with perturbed corners is provided

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

output feedback fault tolerant control by a set theoretic description of ts fuzzy systems this paper is concerned with the observer based output feedback fault tolerant control problem for ts fuzzy systems by constructing a set theoretic description of fuzzy systems the equivalence class theory in set theory is applied for designing observer and controller for less conservative results firstly we designed the observer to get the information of the actuator faults in the system then we use this information to design the fault tolerant controller to compensate for the effect of faults and guarantee stability of the system finally a simple nonlinear massspringdamper system is presented to illustrate the effectiveness of the proposed approach

on computing of arbitrary positive powers for one type of anti tridiagonal matrices of even order abstract in this paper the general expression of the lth power l n where n is the set of positive integers for one type of anti tridiagonal matrices of even order is derived

new exponential estimates for time delay systems this note considers the problem of exponential stability for time delay systems in terms of linear matrix inequalities a new sufficient condition for exponential stability is obtained based on this an improved upper bound of the decay rate can be easily calculated when time varying norm bounded parameter uncertainties appear a new sufficient condition for robust exponential stability of uncertain time delay systems is also provided the reduced conservatism of the proposed conditions is illustrated via two numerical examples

instability of flows in spatially developing media this paper studies specific forms of partial differential equations which represent the amplitude evolution of disturbances to flows in media whose properties vary slowly in space over a length scale epsilon 1 a method is described for finding series solutions in the small parameter epsilon and general results for the green s function and the time periodic response are obtained with the aid of a computer based symbolic algebra manipulation package the method permits results to be obtained to any desired accuracy for any specified spatial variation the method is then applied to find the green s function for the linearized ginzburg landau equation which is a good simple model of instability growth in many marginally unstable fluid dynamical systems in the case where the instability parameter mu normally a constant in the equation varies with the spatial coordinate even though the method produces only power series solutions in epsilon it is shown that with its help exact analytic solutions valid for all epsilon however large can be found in some cases the exact solutions for the cases of linear and quadratic spatial variation of mu are obtained and discussed and criteria are found for the onset of global instability comparisons are made between these criteria and the local absolute and convective instability criteria and the results are found to be in qualitative agreement with other authors numerical and analytic results in particular it is shown that a small region of local absolute instability up to a maximal size which is known analytically may exist and yet that the flow may be globally stable it is also shown that in the case of quadratic spatial variation of mu with an infinite region of local absolute instability the green s function may for some particular parameter ranges become infinite at all spatial locations simultaneously at some finite time

numerical solution of a secular equation a method is proposed for the solution of a secular equation arising in modified symmetric eigenvalue problems and in several other areas this equation has singularities which make the application of standard root finding methods difficult in order to solve the equation a class of transformations of variables is considered which transform the equation into one for which newton s method converges from any point in a certain given interval in addition the form of the transformed equation suggests a convergence accelerating modification of newton s method the same ideas are applied to the secant method and numerical results are presented

robust fuzzy design for nonlinear uncertain stochastic systems via sliding mode control this paper deals with the sliding mode control smc problem for nonlinear stochastic time delay systems by means of fuzzy approach the takagi sugeno t s fuzzy stochastic time delay model with parametric uncertainties and unknown nonlinearities is presented a sufficient condition for the exponential stability in mean square of the sliding motion is also derived moreover it is shown that when the linear matrix inequalities lmis with equality constraint are feasible the designs of both sliding surface and sliding mode controller can be easily obtained via convex optimization a simulation example illustrating the proposed method is given

solving secular and polynomial equations a multiprecision algorithm we present an algorithm for the solution of polynomial equations and secular equations of the form s x 0 for s x i 1 na ix b i 1 0 which provides guaranteed approximation of the roots with any desired number of digits it relies on the combination of two different strategies for dealing with the precision of the floating point computation the strategy used in the package mpsolve of d bini and g fiorentino d a bini g fiorentino design analysis and implementation of a multi precision polynomial rootfinder numer algorithms 23 2000 127 173 and the strategy used in the package eigensolve of s fortune s fortune an iterated eigenvalue algorithm for approximating the roots of univariate polynomials j symbolic comput 33 5 2002 627 646 the algorithm is based on the ehrlich aberth ea iteration and on several results introduced in the paper in particular we extend the concept and the properties of root neighborhoods from polynomials to secular functions provide perturbation results of the roots obtain an effective stop condition for the ea iteration and guaranteed a posteriori error bounds we provide an implementation released in the package mpsolve 3 0 based on the gmp library from the many numerical experiments it turns out that our code is generally much faster than mpsolve 2 0 and of the package eigensolve for certain polynomials like the mandelbrot or the partition polynomials the acceleration is dramatic the algorithm exploits the parallel architecture of the computing platform

on computing of arbitrary positive powers for anti tridiagonal matrices of even order abstract in this paper the general expression of the lth power l n for one type of anti tridiagonal matrices is derived expressions of eigenvectors and jordan s form of the matrix and of the transforming matrix and its inverse are given

delay dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay this paper focuses on the delay dependent stability analysis and stabilization for fuzzy control systems with time delay based on linear matrix inequality lmi approach a delay dependent stability criteria has been developed the design schemes of stabilization via state feedback is developed and then the result is extended to the case of observer based output feedback all the researching results are presented by means of lmis two illustrative examples are given to illustrate the validity of the proposed design procedures

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

exponential estimates for retarded time delay systems an lmi approach exponential estimates and sufficient conditions for the exponential stability of linear time delay systems are given the proof make use of lyapunov krasovskii functionals and the conditions are expressed in terms of linear matrix inequalities

analysis of third order methods for secular equations third order numerical methods are analyzed for secular equations these equations arise in several matrix problems and numerical linear algebra applications a closer look at an existing method shows that it can be considered as a classical method for an equivalent problem this not only leads to other third order methods it also provides the means for a unifying convergence analysis of these methods and for their comparisons finally we consider approximated versions of the aforementioned methods

integer powers of real odd order skew persymmetric anti tridiagonal matrices with constant anti diagonals antitridiag n a c a a r 0 c r in this paper we give the eigenvalue decomposition for real odd order skew persymmetric anti tridiagonal matrices with constant anti diagonals and derive the general expression for integer powers of such matrices

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

powers of complex persymmetric or skew persymmetric anti tridiagonal matrices with constant anti diagonals in this paper we derive a general expression for the entries of the powers of any complex persymmetric or skew persymmetric anti tridiagonal matrix with constant anti diagonals in terms of the chebyshev polynomials of the second kind

generalized updating problems and computation of the eigenvalues of rational toeplitz matrices abstract algebraic and computational properties of the rank one updating of a generalized eigenvalue problem are investigated the results are applied to the computation of the eigenvalues of full toeplitz matrices related to the laurent expansion of a rational function extending a method of handy and barlow already known for the banded toeplitz case

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

robust stabilization of uncertain t s fuzzy time delay systems with exponential estimates this paper deals with the problem of robust stabilization for uncertain takagi sugeno t s fuzzy systems with constant time delays the purpose is to design a state feedback fuzzy controller such that the closed loop system is robustly exponentially stable with a prescribed decay rate sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities lmis by using feasible solutions of these lmis desired fuzzy controllers are designed and their corresponding exponential estimates are given in addition the main results of this paper are explicitly dependent on the decay rate this enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

delay dependent lmi conditions for stability and stabilization of t s fuzzy systems with bounded time delay this paper studies the stability and stabilization problems for time delay nonlinear systems through takagi sugeno t s fuzzy model approach the time delays are assumed to be bounded but perhaps non smooth delay dependent conditions are presented in terms of lmis illustrative examples are given to show the effectiveness and merits of the present results

passivity analysis and passive control of fuzzy systems with time varying delays this paper is concerned with the passive controller design problem for a class of continuous time takagi sugeno t s fuzzy systems with both state and input delays the delays are assumed to be time varying and differentiable a notion of very strict passivity is adopted the purpose is to design a state feedback fuzzy controller such that the resulting closed loop system is very strictly passive vsp delay dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time delay systems and fuzzy systems these conditions are expressed by means of strict linear matrix inequalities lmis that can be easily solved a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method

a constrained eigenvalue problem in this paper we consider the following mathematical and computational problem given the quantities a n m by n m matrix symmetric n 0 n n m by m matrix with full rank t vector of dimension m with nt t 1 determine an x such that operatorname x t ax min subject to the constraints n t x t i x t x 1 ii variants of this problem occur in many applications 1 5 7 8 11 the problem has been studied previously when t 0 the null vector cf 4 6 when t 0 then the problem becomes more complicated

a numerical comparison of methods for solving secular equations numerical comparisons are carried out by the most prominent methods both second and higher order for solving secular equations these equations arise in several matrix problems and numerical linear algebra applications in addition to the comparisons we propose a new starting point our results show a clear advantage to higher order methods

integer powers of real even order anti tridiagonal hankel matrices of the form antitridiagn a c a in this paper we give the eigenvalue decomposition for one type of real even order anti tridiagonal hankel matrices and derive the general expression for integer powers of such matrices

fully nonlinear global modes in spatially developing media abstract global modes on a doubly infinite one dimensional domain wkbj approximations in the linear and nonlinear regions through appropriate transition layers the real global frequency is determined by requiring that spatial branches issuing from x and x be continuously connected at a saddle point of the local nonlinear dispersion relation n l k r 2 x between the frequency the wave number k and amplitude r at a given station x the results constitute a fully nonlinear generalization of the linear frequency selection criteria previously obtained by chomaz et al 1991 monkewitz et al 1993 and le dizes et al 1996

accurate eigenvalue decomposition of real symmetric arrowhead matrices and applications abstract we present a new algorithm for solving the eigenvalue problem for an n n real symmetric arrowhead matrix the algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in o n 2 operations under certain circumstances the algorithm is based on a shift and invert approach only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision each eigenvalue and the corresponding eigenvector can be computed separately which makes the algorithm adaptable for parallel computing our results extend to hermitian arrowhead matrices real symmetric diagonal plus rank one matrices and singular value decomposition of real triangular arrowhead matrices

slowly varying fully nonlinear wavetrains in the ginzburg landau equation abstract following the ideas of howard and kopell 9 a perturbation theory is developed for slowly varying fully nonlinear wavetrains i e solutions which appear locally as travelling waves but with frequencies and wavelengths which may vary widely on long length and time scales this perturbation theory is applied to the ginzburg landau equation the motion and stability of slowly varying wavetrains is shown to be governed by a simple wave equation which can develop shocks corresponding to rapid changes in wavenumber numerical results supporting this theory are presented a shock structure is proposed and numerically verified these results together with a winding invariant valid in the limit of slow variation suggest that over a large range of parameters many initial conditions relax to uniform wavetrains the evolution of a marginally diffusively stable wavetrain is also examined it is argued that the evolution is governed by a perturbed korteweg de vries equation

a new recursive algorithm for inverting general tridiagonal and anti tridiagonal matrices in the current article the authors present a new recursive symbolic computational algorithm for inverting general tridiagonal and anti tridiagonal matrices an illustrative example is given

bifurcation to fully nonlinear synchronized structures in slowly varying media the selection of fully nonlinear extended oscillating states is analyzed in the context of one dimensional nonlinear evolution equations with slowly spatially varying coefficients on a doubly infinite domain two types of synchronized structures referred to as steep and soft global modes are shown to exist steep global modes are characterized by the presence of a sharp stationary front at a marginally absolutely unstable station and their frequency is determined by the corresponding linear absolute frequency as in dee langer propagating fronts soft global modes exhibit slowly varying amplitude and wave number over the entire domain and their frequency is determined by the application of a saddle point condition to the local nonlinear dispersion relation the two selection criteria are compared and shown to be mutually exclusive the onset of global instability first gives rise to a steep global mode via a saddle node bifurcation as soon as local linear absolute instability is reached somewhere in the medium as a result such self sustained structures may be observed while the medium is still globally stable in a strictly linear approximation soft global modes only occur further above global onset and for sufficiently weak advection the entire bifurcation scenario and state diagram are described in terms of three characteristic control parameters the complete spatial structure of nonlinear global modes is analytically obtained in the framework of wkbj approximations 2001 elsevier science b v all rights reserved

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

new delay dependent stabilization conditions of t s fuzzy systems with constant delay this paper focuses on the problem of robust control for takagi sugeno t s fuzzy systems with time delay the delay dependent stability analysis and controller synthesis have been addressed the free weighting matrix method has been used for stability analysis and controller synthesis new and less conservative delay dependent stability conditions are proposed in terms of linear matrix inequalities lmi finally some examples are given to illustrate the effectiveness of the proposed approaches

powers of real persymmetric anti tridiagonal matrices with constant anti diagonals in this paper we present an eigenvalue decomposition with an orthogonal eigenvector matrix for any real persymmetric anti tridiagonal matrix with constant anti diagonals furthermore we derive a general expression for the entries of the powers of these anti tridiagonal matrices in terms of the chebyshev polynomials of the second kind

integer powers of anti tridiagonal matrices of the form antitridiag n a 0 b a b r in this paper we use chebyshev polynomials to derive a general expression for integer powers of real anti tridiagonal matrices with constant anti diagonals and null northeast to southwest diagonal

forward stable eigenvalue decomposition of rank one modifications of diagonal matrices abstract we present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank one modification of a diagonal matrix the algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy in o n operations the algorithm is based on a shift and invert approach only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision each eigenvalue and the corresponding eigenvector can be computed separately which makes the algorithm adaptable for parallel computing our results extend to the complex hermitian case the algorithm is similar to the algorithm for solving the eigenvalue problem for real symmetric arrowhead matrices from n jakovcevic stor et al 2015 16

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

absolute and convective instabilities front velocities and global modes in nonlinear systems abstract we study the existence of self sustained saturated solutions of the real ginzburg landau equation subject to a boundary condition at x 0 such solutions are called nonlinear global ng modes the ng instability referring to the existence of these solutions is rigorously determined and the scaling behavior of the ng modes close to threshold is derived the ng instability is first compared to the linear concept of convective absolute c a instability characterizing whether the impulse response of an unstable flow in an infinite domain is asymptotically damped or amplified at a fixed location ng modes are shown to exist while at the same time the flow may be linearly stable convectively unstable or absolutely unstable the growth size of the ng modes is shown to be proportional to 1 2 when ng and a instabilities exist simultaneously being the criticality parameter whereas a ln 1 scaling is found when the ng instability occurs while the flow is c unstable or linearly stable the nonlinear convective absolute nc na instability defined chomaz 1992 by considering in infinite homogeneous domains whether the front separating a bifurcated state from the basic state moves downstream or upstream is determined using van saarloos and hohenberg 1992 results for the selected front velocity remarkably the na domain and the ng domain are shown to coincide similar results are presented for supercritical bifurcating systems for the van der pol duffing system and for a transcritical model in all the cases the a instability is only a sufficient condition for the existence of an ng mode and these simple models demonstrate that a system may be nonlinearly absolutely unstable whereas it is linearly convectively unstable this property should be generic if one accepts the conjecture that the selected front velocity is always larger than the linear front velocity response to a constant forcing applied at the origin is also studied it is shown that in the ng region the system possesses intrinsic dynamics which cannot be removed by the forcing by contrast the behavior of a nonlinear spatial amplifier is observed in a domain larger than the nc region nc instability is only a sufficient condition to trigger the system with forcing

nonnegative and positive definiteness of matrices modified by two matrices of rank one abstract necessary and sufficient conditions are given for the nonnegative and positive definiteness of matrices of the form a a 1 a 1 a 2 a 2 and a a 1 a 1 a 2 a 2 where a is a hermitian matrix and a 1 a 2 are complex vectors they are derived using some auxiliary results which seem to be of independent interest as well some particular cases of these conditions are also discussed especially in the context of related results known in the literature