continuous takagi sugeno s models reduction of the number of lmi conditions in various fuzzy control design technics fuzzy models of the takagi sugeno type enable representation of a wide class of nonlinear models conditions about their stabilization can be derived systematically usually these conditions are written as linear matrix inequality lmi problems in this paper we use a collection of properties concerning matrices to extend the area of solutions involving the feedback control laws we will work out with continuous fuzzy models and supply results about the stabilization the regulator problem and also hinfin control solutions based on a reduced number of decision variables implying a reduced number of lmi conditions are also proposed we show that a good tradeoff can been obtained

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

on the fourier transform of bessel functions over complex numbers i the spherical case in this note we prove a formula for the fourier transform of spherical bessel functions over complex numbers viewed as the complex analogue of the classical formulae of hardy and weber the formula has strong representation theoretic motivations in the waldspurger correspondence over the complex field

robust h 2 and h control of discrete time systems with polytopic uncertainties via dynamic output feedback this paper addresses the problem of robust h 2 and h control of discrete linear time invariant lti systems with polytopic uncertainties via dynamic output feedback the problem has been known to be difficult when a parameter dependent lyapunov function is to be applied for a less conservative design due to non convexity our approach is based on a novel bounding technique that converts the non convex optimization into a convex one together with a line search which is simple but may be conservative to further reduce the design conservatism an algorithm based on the sequentially linear programming method slpmm is proposed a numerical example is given which demonstrates the feasibility of the proposed design methods

well posedness of feedback systems insights into exact robustness analysis and approximate computations this paper establishes a framework for robust stability analysis of linear time invariant uncertain systems the uncertainty is assumed to belong to an arbitrary subset of complex matrices the concept used here is well posedness of feedback systems leading to necessary and sufficient conditions for robust stability based on this concept some insights into exact robust stability conditions are given in particular frequency domain and state space conditions for well posedness are provided in terms of hermitian form inequalities it is shown that these inequalities can be interpreted as small gain conditions with a generalized class of scalings given by linear fractional transformations lft using the lft scaled small gain condition in the state space setting the duality is established between the h sub spl infin norm condition with frequency dependent scalings and the parameter dependent lyapunov condition connections to the existing results including the structured singular value and the integral quadratic constraints are also discussed finally we show that our well posedness conditions can be used to give a less conservative yet computable bound on the real structured singular value this result is illustrated by numerical examples

a descriptor system approach to robust stability analysis and controller synthesis this note revisits the problem of robust stability analysis and synthesis via parameter dependent lyapunov functions a descriptor system approach is taken to deriving linear matrix inequality conditions for robust stability and robust stabilizability of the polytopic systems and the affine parameter systems under these robust stabilizability conditions state feedback laws that achieve robust stabilization are also constructed the developed results can be viewed as a continuous time counterpart of the discrete time results by oliveira et al the effectiveness of the proposed analysis and synthesis approach is demonstrated by numerical examples

required relationship between objective function and pareto frontier orders practical implications it is well known that the weighted sum aggregate objective function fails to capture pareto points that are located on a concave region of the pareto frontier conditions are established for a general aggregate objective function to capture points on a concave pareto frontier region specifically these conditions are developed in terms of the relative orders of the pareto frontier and aggregate objective function these critical conditions can be used in practice to allow an aggregate objective function to capture any potentially desirable pareto point conversely failure to satisfy these critical conditions can represent a pivotal failure point of the general application of design optimization because we may fail to obtain the design we seek

new characterisations of positive realness and static output feedback control of discrete time systems this article is concerned with the problems of positive real analysis and control synthesis for discrete time systems new linear matrix inequality lmi characterisations of positive realness are derived which enable one to check the positive realness by using parameter dependent lyapunov function the relationship between the proposed characterisations and the existing ones are clarified which shows that our new results are of less conservatism for characterising the positive realness of discrete time systems with polytopic uncertainty in addition sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities numerical examples are included for illustration

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

robust adaptive l2 gain control of polytopic mimo lti systems lmi results passification based direct adaptive control is considered for polytopic uncertain linear time invariant multi input multi output systems linear matrix inequality based results are provided to guarantee that the adaptive algorithm passifies the system whatever the uncertain parameters in some given set the contributions are based on the introduction of a parallel feed forward shunt that liberates from the strong equality constraint pb c t g t often used for strict passification the shunt combined with the introduction of slack variables allows to conclude with easy to test conditions without restrictions on which data is uncertain in the process model the resulting adaptive control is such that the control gain is bounded in a chosen set whatever bounded disturbances moreover it proves to be not worse than computable parameter dependent static output feedback controls with respect to l2 gain attenuation a simple academic example illustrates the results keywords passivity robustness adaptive control lmi output feedback polytopic systems l2 gain

stability of uncertain systems using lyapunov functions with non monotonic terms abstract this paper is concerned with the problem of robust stability of uncertain linear time invariant systems in polytopic domains the main contribution is to present a systematic procedure to check the stability of the uncertain systems by using an arbitrary number of quadratic functions within higher order derivatives of the vector field in the continuous time case and higher order differences of the vector field in the discrete time case the matrices of the lyapunov function appear decoupled from the dynamic matrix of the system in the conditions this fact leads to sufficient conditions that are given in terms of linear matrix inequalities defined at the vertices of the polytope the proposed method does not impose sign condition constraints in the quadratic functions that compose the lyapunov function individually moreover some of the quadratic functions do not decrease monotonically along trajectories however if the sufficient conditions are satisfied then a monotonic standard lyapunov function that depends on the dynamics of the uncertain system can be constructed a posteriori numerical examples from the literature are provided to illustrate the proposed approach

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

robust stability and performance of linear time varying systems in polytopic domains a sufficient condition to assess the stability of linear time varying systems in polytopic domains is given in this paper this condition is written as a feasibility test of linear matrix inequalities expressed at the polytope vertices and taking bounds on the time derivatives of the system parameters into account differently from other techniques in the literature there is no need of gridding procedures on the parameter space neither restrictive assumptions on the uncertainty structure the proposed test can be solved in polynomial time yielding as solution a parameter dependent lyapunov function that assures the system stability moreover the results can be applied to systems with affine parameter uncertainty and can be easily extended to deal with guaranteed cost computation numerical examples show that the proposed condition can lead to less conservative evaluations of the stability domain and of the performance index for this class of systems when compared to the results based on the conventional

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

an lmi condition for the robust stability of uncertain continuous time linear systems a new sufficient condition for the robust stability of continuous time uncertain linear systems with convex bounded uncertainties is proposed in this note the results are based on linear matrix inequalities lmis formulated at the vertices of the uncertainty polytope which provide a parameter dependent lyapunov function that assures the stability of any matrix inside the uncertainty domain with the aid of numerical procedures based on unidimensional search and the lmis feasibility tests a simple and constructive way to compute robust stability domains can be established

lmi characterization of structural and robust stability the discrete time case abstract this paper extends to the discrete time case some robust stability conditions recently obtained for continuous time systems those conditions are expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable as in the continuous time case parameter dependent lyapunov functions can be constructed and consequently the new approach can yield much sharper and less conservative results than the simultaneous stability approach in particular well known stability problems namely d stability and robust stability in the presence of diagonally structured uncertainty can be more efficiently addressed numerical examples are included to illustrate the advantages of the new stability conditions

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

special decentralized control problems in discrete time interconnected systems composed of two subsystems in this paper some special decentralized control problems are addressed for discrete time interconnected systems first it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases then a special kind of decentralized control problem is studied this kind of problem can be viewed as harmonic control among independent subsystems research results show that two unstable systems can generate a stable system through some effective cooperations in addition a decentralized controller design method based on linear matrix inequality is also given by using parameter dependent lyapunov function method developed for the study of robust stability a special linear star coupled dynamical network is also considered the central subsystem must be unstable to stabilize the whole network under a special coupling several examples are given to illustrate the results

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

a new bounded real lemma representation for the continuous time case a differential linear matrix inequality dlmi approach is introduced for the solution of various linear continuous time control problems the proposed method permits the application of linear matrix inequalities lmis to the solution of control design problems under uncertainty these problems are solved for finite horizon linear systems while considerably reducing the overdesign inherent in previous methods the new approach also allows for the solution of the output feedback control problem for systems belonging to a finite set of uncertain plants with hardly any overdesign four examples are given to demonstrate the applicability of the new method

robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties this paper studies the static output feedback sof control problem of continuous time linear systems with polytopic uncertainties novel lmi conditions with a line search over a scalar variable for designing robust sof controllers are proposed where the uncertain output matrix of the considered system is allowed to be not of full row rank in particular it is shown that the new method can give less or at least the same conservative results than those methods by inserting a matrix equality constraint between system output matrix and lyapunov matrix furthermore the result is extended to the case of h control numerical examples are given to illustrate the effectiveness of the proposed method

brief paper comparisons among robust stability criteria for linear systems with affine parameter uncertainties this paper is concerned with the problem of comparisons among robust stability criteria for a class of uncertain linear systems where the system state matrices considered are affinely dependent on the uncertain parameters at first a robust stability criterion for the class of systems to be affinely quadratically stable aqs is derived based on the vertex separator approach where affine parameter dependent lyapunov functions are exploited to prove stability then comparison results between the robust stability criterion and the existing tests for aqs are given in terms of degree of conservatism a numerical example is given to illustrate the results

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

robust discrete time simple adaptive regulation robust simple adaptive controllers are proposed for regulation of linear discrete time systems with parameter uncertainties sufficient conditions for closed loop stability of the proposed control scheme are derived these lead to the requirement of almost strictly positive realness of the plant which is shown to be equivalent under certain conditions to a minimum phase requirement a numerical example is given that demonstrates the applicability of the proposed method and the simplicity of its implementation

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

static output feedback control synthesis for linear systems with time invariant parametric uncertainties this technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous time systems with time invariant polytopic uncertainties sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities furthermore the results are also extended to h2 static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods

brief stability analysis of discrete time systems with actuator saturation by a saturation dependent lyapunov function in this paper stability of discrete time linear systems subject to actuator saturation is analyzed using a saturation dependent lyapunov function this saturation dependent lyapunov function captures the real time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction which is based on the solution of an lmi optimization problem numerical examples are presented to show the effectiveness of the proposed method

lmi tests for positive definite polynomials slack variable approach the considered problem is assessing non negativity of a function s values when indeterminates are in domains constrained by scalar polynomial inequalities the tested functions are multi indeterminates polynomial matrices which are required to be positive semi definite new tests based on linear matrix inequalities are provided in a slack variables type approach the results are compared to those obtained via the sum of squares approach they are proved to be equivalent in case of unbounded domains and less conservative if polytopic type bounds are known

robust matrix root clustering analysis through extended kyp lemma this paper is dedicated to robust matrix eigenvalue clustering in a subregion mathcal d of the complex plane a norm bounded uncertainty is considered cd is any intersection and or union of half planes discs and outsides of discs this work aims at computing the associated complex cd stability radius this challenge was already tackled in a recent paper but the technique therein may fail or lead to conservative results when the subregions overlap the present paper proposes to circumvent those limits thanks to an extended version of the kalman yakubovich popov kyp lemma which is deduced from the so called generalized s procedure

kuznetsov formulas for real rank one groups abstract a generalization of kuznetsov s formula is given for line bundles over complete riemannian locally symmetric spaces of rank 1 and of finite volume in the classical case of riemann surfaces the methods yields a new proof of proskurin s generalization of kuznetsov s formula

static output feedback of state multiplicative systems with application to altitude control a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with stochastic multiplicative wiener type noise that achieves a minimum bound on either the stochastic h 2 or the h performance level is introduced a solution is achieved also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope the stochastic uncertainties appear in both the dynamic and the measurement matrices of the system the problems are solved using the expected value of the standard performance index over the stochastic parameters the theory developed is applied to an altitude control example

improved lmi representations for the analysis and the design of continuous time systems with polytopic type uncertainty simple modifications to the representation of the bounded real lemma brl in the linear continuous time invariant case are introduced these modifications reduce the overdesign that occurs in the analysis and the design of systems with polytopic type uncertainties a different lyapunov function accompanies each of the vertices of the uncertainty polytope thus eliminating the need for quadratic stability or stabilizability the advantages of these new representations are demonstrated by way of two examples

an lmi approach to d stability and d stabilization of linear discrete singular systems with state delay abstract the problems of d stability and d stabilization for linear discrete singular systems with state delay are addressed in this paper by using the state augmentation technique a necessary and sufficient d stability condition and a sufficient d stabilization condition for linear discrete singular time delay systems are firstly proposed then based on these conditions quadratic d stability and d stabilization conditions for linear discrete singular time delay systems with norm bounded uncertainties and interval uncertainties are obtained respectively both the d stability and d stabilization conditions are proposed in terms of linear matrix inequalities finally illustrative examples show that the proposed conditions are effective to check the d stability and to design the d stabilizing controller for linear discrete singular time delay systems

normal constraint method with guarantee of even representation of complete pareto frontier multiobjective optimization is rapidly becoming an invaluable tool in engineering design a particular class of solutions to the multiobjective optimization problem is said to belong to the pareto frontier a pareto solution the set of which comprises the pareto frontier is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other accordingly the pareto frontier plays an important role in engineering design it characterizes the tradeoffs between conflicting design objectives some optimization methods can be used to automatically generate a set of pareto solutions from which a final design is subjectively chosen by the designer for this approach to be successful the generated pareto set must be truly representative of the complete optimal design space pareto frontier in other words the set must not overrepresent one region of the design space or neglect others some commonly used methods comply with this requirement whereas others do not this paper offers a new phase in the development of the normal constraint method which is a simple approach for generating pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives the even distribution of the generated pareto solutions can facilitate the process of developing an analytical expression for the pareto frontier in n dimension an even distribution of pareto solutions also facilitates the task of choosing the most desirable final design from among the set of pareto solutions the normal constraint method bears some similarities to the normal boundary intersection and constraint methods importantly the developments presented in this paper define its critical distinction namely the ability to generate a set of evenly distributed pareto solutions over the complete pareto frontier examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method as well as with the original normal constraint method

simplified adaptive control via improved robust positive real conditions a new method is derived for embedding plants in a robust state feedback scheme to achieve strictly positive realness of the resulting augmented plants a state feedback gain is derived that guarantees the strictly positive realness of the closed loop in presence of polytopic type possibly time varying parameter uncertainties in the model that describes the plant this is achieved by assigning different lyapunov functions to each of the vertices of the uncertainty polytope the obtained feedback gain is used to apply existing methods for robust simplified adaptive control on systems with possibly time varying polytopic uncertainties

an lmi approach to stability analysis of coupled parabolic systems we analyze the exponential stability of a class of distributed parameter systems the system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients we approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis using a quadratic lyapunov function we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities

stochastic passivity and its application in adaptive control a positive real like lemma for finite dimensional linear time invariant uncertain systems with state multiplicative noise is derived the system uncertainties are assumed to be of either polytopic or markov jump type passivity conditions for both cases are derived in terms of linear matrix inequalities the results are used to the design a direct adaptive controller for a tracking system

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

brief positive polynomial matrices and improved lmi robustness conditions recently several new lmi conditions for stability of linear systems have been proposed introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions and intractable non convex robust stability conditions in this paper we show that these improved lmi conditions can be derived with the help of some basic results on positive polynomial matrices the approach allows us to derive in a unifying way results in the state space and polynomial frameworks applications to robust stability analysis and robust stabilization of systems with multi linear parametric uncertainty are fully described

on the kuznetsov trace formula for pgl2 c abstract in this note using a representation theoretic method of cogdell and piatetski shapiro we prove the kuznetsov trace formula for an arbitrary discrete group in pgl 2 c that is cofinite but not cocompact an essential ingredient is a kernel formula recently proved by the author on bessel functions for pgl 2 c this approach avoids the difficult analysis in the existing method due to bruggeman and motohashi

parameter and controller dependent lyapunov functions for robust d stability and robust performance controller design this paper addresses the design of output controllers of chosen order in a given set for ensuring a number of desired properties such as robust d stability and robust performance it is shown that a sufficient condition for determining such controllers can be obtained by solving convex optimization problems with linear matrix inequality constraints through the introduction of a lyapunov function depending polynomially on both uncertainty and controller the proposed condition is also necessary for sufficiently large degrees of the polynomials involved under some assumptions

a new decentralised controller design method for a class of strongly interconnected systems abstractin this paper two interconnected structures are first discussed under which some closed loop subsystems must be unstable to make the whole interconnected system stable which can be viewed as a kind of strongly interconnected systems then comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown a new approach for the design of decentralised controllers is presented by determining the lyapunov function structure previously which allows the existence of unstable subsystems by fully utilising the orthogonal space information of input matrix some new understandings are presented for the construction of lyapunov matrix this new method can deal with decentralised state feedback static output feedback and dynamic output feedback controllers in a unified framework furthermore in order to reduce the design conservativeness and deal with robustness a new robust decentralised controller design method is given by combining with the parameter depend

robust stability functionals of state delayed systems with polytopic type uncertainties via parameterdependent lyapunov functions this paper considers the problem of robust stability for linear systems with a constant time delay in the state and subject to real convex polytopic uncertainty both delay independent and delay dependent stability conditions are characterized by linear matrix inequalities which allow the use of parameter dependent lyapunov functionals to analyse the system stability against parameter perturbations and therefore improve the conservativeness resulting from the single lyapunov functional in order to determine the maximum of time delay within which the system remains stable the problem can be cast into a generalized eigenvalue problem and solved by standard lmi solvers two examples are included to illustrate the proposed method

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

a method for generating a well distributed pareto set in nonlinear multiobjective optimization a method is presented for generating a well distributed pareto set in nonlinear multiobjective optimization the approach shares conceptual similarity with the physical programming based method the normal boundary intersection and the normal constraint methods in its systematic approach investigating the objective space in order to obtain a well distributed pareto set the proposed approach is based on the generalization of the class functions which allows the orientation of the search domain to be conducted in the objective space it is shown that the proposed modification allows the method to generate an even representation of the entire pareto surface the generation is performed for both convex and nonconvex pareto frontiers a simple algorithm has been proposed to remove local pareto solutions the suggested approach has been verified by several test cases including the generation of both convex and concave pareto frontiers

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

robust admissibility of uncertain switched singular systems this article investigates the robust admissibility of uncertain discrete time switched singular systems first the admissibility is introduced by using the switched lyapunov function for singular systems sufficient conditions for robust admissibility of uncertain switched singular systems are presented in strict linear matrix inequalities formulation robust admissibility condition designs for both state feedback and static output control feedback are then derived numerical examples are provided to illustrate our approach

dilated lmi conditions for time varying polytopic descriptor systems the discrete time case this article addresses the admissibility analysis and state feedback control synthesis problems of discrete time polytopic descriptor systems with possibly time varying parameters first we present a new necessary and sufficient strict linear matrix inequality lmi condition for the admissibility analysis of linear time invariant lti descriptor systems then based on the concept of poly quadratic admissibility introduced in this article we extend this result to the admissibility analysis of possibly time varying parameter dependent descriptor systems this extension which applies to both uncertain and measurable parameters uses parameter dependent lyapunov functions and employs two slack variables the extended conditions are also expressed as strict lmi conditions which are easily tractable numerically compared to the non strict ones often encountered when dealing with descriptor systems note that we have proposed two separate admissibility analysis conditions one directly exploitable for stat

parameter dependent stability and stabilization of uncertain time delay systems a new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays the parameters of the system are not exactly given they are known to reside in a given polytope the test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope this condition is parameter dependent and it therefore improves previous results that were derived using a single lyapunov krasovskii functional the stability test is readily extended to provide a criterion for robust stabilization via state feedback

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

brief an lmi condition for robust stability of polynomial matrix polytopes a sufficient lmi condition is proposed for checking robust stability of a polytope of polynomial matrices it hinges upon two recent results a new approach to polynomial matrix stability analysis and a new robust stability condition for convex polytopic uncertainty numerical experiments illustrate that the condition narrows significantly the unavoidable gap between conservative tractable quadratic stability results and exact np hard robust stability results

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

a new design of robust h2 filters for uncertain systems abstract in this paper a structured polynomial parameter dependent approach is proposed for robust h 2 filtering of linear uncertain systems given a stable system with parameter uncertainties residing in a polytope with s vertices the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain a new polynomial parameter dependent idea is introduced to solve the robust h 2 filtering problem which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain or the linearly parameter dependent framework that uses linear convex combinations of s matrices this idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices linear matrix inequality lmi conditions are obtained for the existence of admissible filters and based on these the filter design is cast into a convex optimization problem which can be readily solved via standard numerical software both continuous and discrete time cases are considered the merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods as shown both theoretically and through extensive numerical examples

periodic memory state feedback controller new formulation analysis and design results this paper proposes a unified setup for robust stability and performance analysis and synthesis for periodic polytopic discrete time systems relying on a general formulation for state feedback periodic memory controllers and a new time lifting new sufficient lmi conditions for the existence of robust stability certificates and h2 guaranteed cost control laws are derived comparisons of the efficiency of different controller structures illustrate these developments on a numerical example

fundamental connections among the stability conditions using higher order time derivatives of lyapunov functions for the case of linear time invariant systems abstract it has already been recognized that looking for a positive definite lyapunov function such that a high order linear differential inequality with respect to the lyapunov function holds along the trajectories of a nonlinear system can be utilized to assess asymptotic stability when the standard lyapunov approach examining only the first derivative fails in this context the main purpose of this paper is on one hand to theoretically unveil deeper connections among existing stability conditions especially for linear time invariant lti systems and from the other hand to examine the effect of the higher order time derivatives approach on the stability results for uncertain polytopic lti systems in terms of conservativeness to this end new linear matrix inequality lmi stability conditions are derived by generalizing the concept mentioned above and through the development relations among some existing stability conditions are revealed examples illustrate the improvement over the quadratic approach

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

a less conservative lmi condition for robust cal d stability of polynomial matrix polytopes a projection approach this technical note investigates the problem of checking robust d stability of a polytope of polynomial matrices finsler s projection lemma is taken to derive a new sufficient condition in terms of a linear matrix inequality lmi feasibility problem the basic idea behind this condition is to lift the existing stability condition into the one of larger space by means of finsler s lemma and based on it to introduce additional decision variables examples are given to show that the proposed condition can yield less conservative results than the previous one

brief paper parameter dependent robust h filtering for uncertain discrete time systems this paper is concerned with the problem of parameter dependent h filtering for discrete time systems with polytopic uncertainties the uncertain parameters are supposed to reside in a polytope being different from previous results in the quadratic framework the parameter dependent lyapunov function is used in this paper both full and reduced order filters are designed which guarantee the asymptotic stability and a prescribed h performance level the filter parameters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

parameter dependent robust stability of uncertain time delay systems this paper presents a new delay dependent and parameter dependent robust stability criterion for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state this criterion expressed as a set of linear matrix inequalities requires no matrix variable to be fixed for the entire uncertainty polytope which produces a less conservative stability test result numerical examples are given to show the effectiveness of the proposed techniques

technical communique new dilated lmi characterizations for continuous time multiobjective controller synthesis this paper provides new dilated linear matrix inequality lmi characterizations for continuous time controller synthesis the dilated lmis enable us to parametrize controllers without involving the lyapunov variables in the parametrizations taking advantage of this feature we can readily design multiobjective controllers with non common lyapunov variables whereas we are forced to employ a common one in the well known lyapunov shaping paradigm in particular it is shown that the proposed dilated lmi based approach to h 2 d stability synthesis encompasses the corresponding lyapunov shaping paradigm as a special case in this sense the results of this paper can be viewed as partial counterparts of those obtained in the discrete time setting

mathematical and pragmatic perspectives of physical programming physical programming pp is an emerging multiobjective and design optimization method that has been applied successfully in diverse areas of engineering and operations research the application of pp calls for the designer to express preferences by defining ranges of differing degrees of desirability for each design metric although this approach works well in practice it has never been shown that the resulting optimal solution is not unduly sensitive to these numerical range definitions pp is shown to be numerically well conditioned and its sensitivity to designer input with respect to optimal solution is compared with that of other popular methods the important proof is provided that all solutions obtained through pp are pareto optimal and the notion of pareto optimality is extended to one of pragmatic implication the important notion of p dominance that extends the concept of pareto optimality beyond the cases minimize and maximize is introduced p dominance is shown to lead to the important concept of generalized pareto optimality numerical results are provided that illustrate the favorable numerical properties of physical programming

robust performance analysis with lmi based methods for real parametric uncertainty via parameter dependent lyapunov functions robust performance analysis for linear time invariant systems with linear fractional transformation real parametric uncertainty is considered new conditions of robust stability performance based on parameter dependent lyapunov functions are proposed the robust stability performance measures are robust pole location robust h sub spl infin performance and robust h sub 2 performance linear matrix inequality lmi based sufficient conditions for the existence of parameter dependent lyapunov functions are derived by using the quadratic separation concept the performances of the proposed conditions are compared with existing tests