exponential stabilization of a class of nonlinear systems a generalized gronwall bellman lemma approach in this paper stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized gronwall bellman lemma approach the nonlinear systems under consideration can be non lipschitz two cases are treated for the exponential stabilization the static state feedback and the static output feedback the robustness of the proposed control laws with regards to parameter uncertainties is also studied a numerical example is given to show the effectiveness of the proposed method

new solution method of linear static output feedback design problem for linear control systems abstract a new method of construction of the linear static output feedback for linear control systems is offered the essence of this method consists in construction of an initial approximation of the feedback matrix such that a numerical sequence which generated by arbitrary iterative method and beginning from this initial approximation converges to an exact solution of the feedback design problem examples are given

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

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

proof of a conjecture of sarwate and pursley regarding pairs of binary m sequences binary m sequences are maximal length sequences generated by shift registers of length m that are employed in navigation radar and spread spectrum communications systems because of their crosscorrelation properties it is well known that given a pair of distinct m sequences the crosscorrelation function must take on at least three values the article considers crosscorrelation functions that take on exactly three values and where these values are preferred in that they are small the main result is a proof of a conjecture made by sarwate and pursley in 1980 that if m spl equiv 0 mod 4 then there are no preferred pairs of binary m sequences the proof makes essential use of a deep theorem of mceliece 1971 that restricts the possible weights that can occur in a binary cyclic code

a hamilton jacobi setup for the static output feedback stabilization of nonlinear systems the local static output feedback stabilization problem for a class of nonlinear affine systems is discussed a sufficient condition is es tablished and a partial converse is worked out this condition provides a counterpart to a well known result of linear systems theory the effective ness of the developed theory is illustrated with a simple example

the cross correlation of binary sequences with optimal autocorrelation binary sequences with low correlation have applications in communication systems and cryptography though binary sequences with optimal autocorrelation were constructed in the literature no pair of binary sequences with optimal autocorrelation are known to have also best possible cross correlation in this paper new bounds on the cross correlation of binary sequences with optimal autocorrelation are derived and pairs of binary sequences having optimal autocorrelation and meeting some of these bounds are presented these new bounds are better than the sarwate bounds on the cross correlation of binary sequences with optimal autocorrelation

a heuristic approach to solving a class of bilinear matrix inequality problems abstract many canonical and modern control problems can be recast into the problem of a group of matrix inequalities some of them are in the form of linear matrix inequalities lmis which can be solved very efficiently by the powerful lmi toolbox in matlab but some others are in the form of bilinear matrix inequalities the characteristic of this latter class of problems is that when the so called communicating variables are fixed the overall problem will be reduced to the problem in lmis thus how to find the communicating variables is the key to solve the whole problem in this paper an optimal estimate for the communicating variables is presented we will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems numerical examples are provided to show the effectiveness of the proposed method

periodically time varying memory static output feedback control design for discrete time lti systems this paper addresses the problem of static output feedback sof stabilization for discrete time lti systems we approach this problem using the recently developed periodically time varying memory state feedback controller ptvmsfc design scheme a bilinear matrix inequality bmi condition which uses a pre designed ptvmsfc is developed to design the periodically time varying memory sof controller ptvmsofc the bmi condition can be solved by using bmi solvers alternatively we can apply two steps and iterative linear matrix inequality algorithms that alternate between the ptvmsfc and ptvmsofc designs finally an example is given to illustrate the proposed methods

hybrid robust boundary and fuzzy control for disturbance attenuation of nonlinear coupled ode beam systems with application to a flexible spacecraft this paper introduces a hybrid robust boundary and fuzzy control design for disturbance attenuation of a class of coupled systems described by nonlinear ordinary differential equations odes and two nonlinear beam equations initially a takagi sugeno t s model is employed to exactly represent the nonlinear ode subsystem then a fuzzy controller is designed for the ode subsystem based on the t s fuzzy model and a robust boundary controller via beam boundary measurements is proposed for the nonlinear beam subsystem such a hybrid robust boundary and fuzzy controller is developed in terms of a set of space dependent bilinear matrix inequalities bmis by lyapunov s direct method which can exponentially stabilize the coupled system in the absence of disturbances and achieve an prescribed h infty performance of disturbance attenuation in the presence of disturbances furthermore in order to make the level of disturbance attenuation as small as possible a suboptimal h infty control problem is formulated as a bmi optimization problem a two step procedure is subsequently presented to solve this bmi optimization problem by the existing linear matrix inequality optimization techniques finally the proposed control method is applied to the control of a flexible spacecraft to illustrate its effectiveness

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

minimal norm static feedbacks using dissipative hamiltonian matrices abstract in this paper we characterize the set of static state feedbacks that stabilize a given continuous linear time invariant system pair using dissipative hamiltonian matrices this characterization results in a parametrization of feedbacks in terms of skew symmetric and symmetric positive semidefinite matrices and leads to a semidefinite program that computes a static state stabilizing feedback this characterization also allows us to propose an algorithm that computes minimal norm static feedbacks the theoretical results extend to the static output feedback sof problem and we also propose an algorithm to compute the minimal norm sof we illustrate the effectiveness of our algorithm compared to state of the art methods for the sof problem on numerous numerical examples from the compleib library

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

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

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

stability analysis for linear systems under state constraints this note revisits the problem of stability analysis for linear systems under state constraints new and less conservative sufficient conditions are identified under which such systems are globally asymptotically stable based on these sufficient conditions iterative linear matrix inequality lmi algorithms are proposed for testing global asymptotic stability of the system in addition these iterative lmi algorithms can be adapted for the design of globally stabilizing state feedback gains

a constructive method to static output stabilisation of markov jump systems this paper is concerned with the static output feedback stabilisation of markov jump systems transition probabilities are assumed to be incomplete namely they may be known uncertain with known lower and upper bounds and unknown to linearise the nonlinearities induced by unknown transition probabilities a linearisation is developed to solve the static output feedback problem by means of linear matrix inequalities a constructive method is proposed to separate the controller gain matrices from lyapunov variables based on the linearisation and the separation sufficient conditions are established to guarantee that the closed loop system is stochastically stable by the designed static output feedback controller the obtained results are further extended to deal with norm bounded or polytopic uncertainties on system matrices numerical examples are given to demonstrate the effectiveness of the proposed method

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

output reachable set estimation for switched linear systems and its application in safety verification this paper addresses the output reachable set estimation problem for continuous time switched linear systems consisting of hurwtiz stable subsystems based on a common lyapunov function approach the output reachable set is estimated by a union of bounding ellipsoids then multiple lyapunov functions with time scheduled structure are employed to estimate the output reachable set for switched systems under dwell time constraint furthermore the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation first a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed then the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters numerical examples are provided to illustrate our results

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

mixed h and passive control for singular systems with time delay via static output feedback in this paper the mixed h and passive control problem is studied for singular systems with time delay a sufficient condition is proposed to ensure the considered system to be regular impulse free and stable with mixed h and passivity performance level then the criterion is adopted to design a static output feedback controller in terms of bilinear and linear matrix inequalities an algorithm is established to cast the nonlinear feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

observer based h_ infty sampled data fuzzy control for a class of nonlinear parabolic pde systems in this paper an observer based h infty sampled data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation pde systems with the aid of the modal decomposition technique a nonlinear ordinary differential equation ode model is initially derived to describe the dominant slow dynamics of the pde system subsequently the resulting nonlinear ode model is accurately represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a finite dimensional observer based sampled data fuzzy control design with h infty performance is developed for the pde system via employing a novel time dependent functional the outcome of the observer based h infty sampled data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem moreover an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal h infty sampled data fuzzy controller finally simulation results on the fisher equation and a temperature cooling fin of high speed aerospace vehicle illustrate that the proposed design method is effective

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

robust normalization and stabilization of uncertain descriptor systems with norm bounded perturbations this note is concerned with the problem of the so called quadratic normalization and stabilization via both proportional and derivative state feedback pdsf and proportional and derivative output feedback pdof for uncertain descriptor systems with norm bounded perturbations necessary and sufficient conditions are presented in terms of linear matrix inequalities lmis or quadratic matrix inequalities qmis by using a simple idea of changing the problem to the corresponding stabilization problem of an augmented uncertain system

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

static output feedback controller design for fuzzy systems an ilmi approach this paper examines the problem of static output feedback control of a takagi sugeno ts fuzzy system the existence of a static output feedback control law is given in terms of the solvability of bilinear matrix inequalities an iterative algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain to reduce the conservatism of the design the structural information of the membership function of the fuzzy rules is incorporated numerical examples are used to illustrate the validity of the methods

high order scheme for a nonlinear maxwell system modelling kerr effect this paper is devoted to the derivation of an efficient numerical scheme for the kerr maxwell system we begin by studying the 1 d riemann problem we obtain a result of existence and uniqueness for large data then we develop a high order roe solver and exhibit solutions in 1 d and 2 d simulations

brief paper robust pid controller tuning based on the heuristic kalman algorithm this paper presents a simple but effective tuning strategy for robust pid controllers satisfying multiple h performance criteria finding such a controller is known to be computationally intractable via the conventional techniques this is mainly due to the non convexity of the resulting control problem which is of the fixed order structure type to solve this kind of control problem easily and directly without using any complicated mathematical manipulations and without using too many user defined parameters we utilize the heuristic kalman algorithm hka for the resolution of the underlying constrained non convex optimization problem the resulting tuning strategy is applicable both to stable and unstable systems without any limitation concerning the order of the process to be controlled various numerical studies are conducted to demonstrate the validity of the proposed tuning procedure comparisons with previously published works are also given

brief paper an ilmi approach to robust h2 static output feedback fuzzy control for uncertain discrete time nonlinear systems this paper studies the problem of robust h 2 static output feedback sof fuzzy control for discrete time nonlinear systems with parametric uncertainties the takagi and sugeno fuzzy model is employed to represent an uncertain discrete time nonlinear system a sufficient condition for the existence of robust h 2 sof fuzzy controllers is presented in terms of a set of matrix inequalities which not only guarantees the stability of the closed loop fuzzy system but also provides an upper bound on the quadratic cost function a suboptimal robust h 2 sof fuzzy control problem is addressed in the sense of minimizing the bound an iterative linear matrix inequality ilmi algorithm is proposed to compute the feedback gain matrices of the suboptimal fuzzy controller finally two numerical examples are also provided to demonstrate the effectiveness of the proposed method

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

the geometry of quadrics and correlations of sequences corresp nondegenerate quadrics of pg 2l 2 s have been used to construct ternary sequences of length 2 2sl 1 1 2 s 1 with perfect autocorrelation function the same construction can be used for degenerate quadrics for this case as well as quadrics of pg n q with n arbitrary and q p s for any prime p this is possible because it is shown that if q subseteq rm pg n q is a quadric possibly degenerate that has the same size as a hyperplane then provided q itself is not a hyperplane the hyperplanes of pg n q intersect q in three sizes these sizes depend on whether n is even or odd and the degeneracy of q finally a connection to maximum period linear recursive sequences is made

stability stabilization and l 2 gain analysis of periodic piecewise linear systems in this paper the stability stabilization and l 2 gain problems are investigated for periodic piecewise linear systems in which not all subsystems are hurwitz first some sufficient and necessary conditions for the exponential stability are established by employing a discontinuous lyapunov function with time varying lyapunov matrix stabilization and l 2 gain conditions of periodic piecewise linear systems are proposed by allowing the corresponding lyapunov function to be possibly non monotonically decreasing over a period a state feedback periodic piecewise controller is developed to stabilize the system and the corresponding algorithm is proposed to compute the controller gain the l 2 gain criteria with continuous time varying lyapunov matrix and piecewise constant lyapunov matrices are studied as well numerical examples are given to show the validity of the proposed techniques

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

stabilization of uncertain fuzzy control systems via a new descriptor system approach this paper addresses stabilizing a class of fuzzy control systems with a guaranteed h control performance via a new descriptor system approach based on the sector nonlinearity concept of tanaka and wang 2001 1 the uncertain nonlinear system can be exactly represented by t s fuzzy models then we propose using the composite state and output feedback csaof fuzzy control for the control design a new descriptor fuzzy system will be represented in this paper based on the lyapunov stability theorem and the linear matrix inequality lmi tool we solve the controller gain matrices some positive constants and some common positive definite matrices then we derive two sufficient conditions to stabilize the uncertain fuzzy control systems with guaranteed h control performance moreover the developed h criterion guarantees that the influence of external disturbance is as small as possible a practical system is given to illustrate the validity of the proposed scheme

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

static output feedback control design for linear mimo systems with actuator dynamics governed by diffusion pdes this paper deals with the problem of static output feedback sof control design for a class of diffusion partial differential equation pde and ordinary differential equation ode cascades where the ode model is used to describe the dynamics of the multi input and multi output mimo plant and the diffusion pde model is employed to represent the dynamics of actuators the objective of this paper is to develop a simple as well as effective sof controller via the lyapunov s direct method such that the resulting closed loop system is globally exponentially stable by constructing a quadratic lyapunov function the sufficient condition on the globally exponential stability of the closed loop cascaded system is presented in terms of linear matrix inequality lmi then an lmi based design method of the sof controller is developed on the basis of the obtained stability analysis result finally two numerical examples are provided to illustrate the effectiveness of the proposed design method

robust static output feedback controller synthesis using kharitonov s theorem and evolutionary algorithms this paper presents a simple but effective tuning strategy for robust static output feedback sof controllers with minimal quadratic cost in the context of multiple parametric uncertainties finding this type of controller is known to be computationally intractable using conventional techniques this is mainly due to the non convexity of the resulting control problem which has a fixed structure to solve this kind of control problem easily and directly without using any complicated mathematical manipulations we utilize kharitonov s theorem and an evolutionary algorithm ea for the resolution of the underlying constrained optimization problem using kharitonov s theorem a family of bounded robustly stable static output feedback controllers can be defined and ea is used to select the controller that ensures a minimal quadratic cost within this family the resulting tuning strategy is applicable to both stable and unstable systems without any limitations on the order of the process to be controlled a numerical study was conducted to demonstrate the validity of the proposed tuning procedure

a case study for the open question disturbance decoupling problem for singular systems by output feedback we study the disturbance decoupling problem for singular systems ex spl dot ax bu gd y cx z hx with left invertibility we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupling problem with or without stability by output feedback that also makes the resulting closed loop system regular and or of index at most one all results are proved based on a condensed form that can be computed using orthogonal transformations i e can be computed in a numerically stable way

h_ infty static output feedback control design for discrete time systems using reinforcement learning this paper provides necessary and sufficient conditions for the existence of the static output feedback opfb solution to the h infty control problem for linear discrete time systems it is shown that the solution of the static opfb h infty control is a nash equilibrium point furthermore a q learning algorithm is developed to find the h infty opfb solution online using data measured along the system trajectories and without knowing the system matrices this is achieved by solving a game algebraic riccati equation online and using the measured data a simulation example shows the effectiveness of the proposed method

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

technical communique an improvement on multivariable pid controller design via iterative lmi approach this note improves the results of zheng wang and lee automatica 38 2002 517 on the design of multivariable pid controllers via lmi approach the idea of the improvement is to transform the problem of pid controller design to that of static output feedback sof controller design for a system in descriptor form the merits of the present result are 1 the present condition removes the invertibility constraint on the controllers in zheng et al 2002 and incorporates it to the matrix inequality to be solved 2 once the sof matrix is obtained the pid gains are ready in hand and no additional computation is needed 3 the present approach can deal with the case of some system parameters subject to perturbations

dissipative control for state saturated discrete time varying systems with randomly occurring nonlinearities and missing measurements in this paper the dissipative control problem is investigated for a class of discrete time varying systems with simultaneous presence of state saturations randomly occurring nonlinearities as well as multiple missing measurements in order to render more practical significance of the system model some bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements the purpose of the addressed problem is to design a time varying output feedback controller such that the dissipativity performance index is guaranteed over a given finite horizon by introducing a free matrix with its infinity norm less than or equal to 1 the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities a novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

brief paper stability and h2 objective characterizations in control a comparative study this paper is concerned with stability and h 2 objective characterizations in control new forms of alternative lmi characterizations are presented for continuous time stability and h 2 objective a key relationship between the alternative characterizations for continuous time systems and the existing discrete time versions is illustrated the existing enhanced lmi characterization for continuous time systems called the reciprocal projection lemma is revisited and an alternative proof is provided with a new interpretation an e embedded lmi characterization is presented for a comparative study with the reciprocal projection lemma and for numerical analysis on the conservativeness of synthesis conditions through an application in control it is discussed that when applied to multi objective problems in control the alternative characterizations in this paper lead to an lmi solution with further significant conservativeness reduction compared to the reciprocal projection lemma in addition through the comparison with the existing dilated lmi condition it is shown that the dilated condition is an equivalent continuous time counterpart of the existing discrete time versions

finite time h static output control of markov jump systems with an auxiliary approach this paper considers the finite time h static output feedback control of markov jump systems with the help of introducing two new variables related to the original system state and output sufficient conditions for the closed loop system to be stochastic finite time boundedness with the prescribed h performance level are proposed in terms of linear matrix inequalities lmis meanwhile the static output control gains are solved explicitly by the proposed conditions it is shown that the proposed method is less or at least the same conservative than the existing result lastly a numerical example is given to demonstrate the effectiveness of the proposed method

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

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

stability analysis and synthesis for an affine fuzzy control system via lmi and ilmi a continuous case a new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper the method suggested is based on the numerical convex optimization techniques in analysis the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities lmis the emphasis of this paper however is on the synthesis of fuzzy controller based on the derived stability condition in the synthesis the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains continuous iterative lmi ilmi approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system

a new computational approach to stability analysis and synthesis of linguistic fuzzy control system in this paper stability analysis and synthesis of the type ii singleton type linguistic fuzzy control system are addressed first stability theorems are given for both continuous time case and discrete time case and they are recast in the formulation of bilinear matrix inequalities bmis continuous and discrete iterative linear matrix inequality methods are presented to obtain the feasible solution for the stability conditions represented as the bmi the interesting feature of this paper is that the suggested method can be applied not only to the stability analysis but also to the controller synthesis when it is applied to the synthesis of the type ii fuzzy logic controller the resulting one can theoretically guarantee the stability of the closed loop system finally the effectiveness of the suggested method is illustrated via computer simulation

global stabilization for linear continuous time varying systems in this paper stabilization problem via static output feedback controls for linear time varying systems is investigated based on the lyapunov function techniques we show that for linear time varying systems the global null controllability guarantees the output feedback stabilization the verifiable stabilizability conditions and output feedback control design are stated the result can be applicable to the output feedback stabilizability of a class of nonlinear time varying systems numerical examples illustrated the conditions are given

static output feedback stabilization with h sub spl infin performance for linear discrete time systems this note presents a new sufficient condition for the static output feedback stabilization of linear discrete time systems this new condition is expressed as a linear matrix inequality feasibility problem and hence easily tractable numerically an extension of this condition is given in order to incorporate h sub spl infin performance objectives the applicability of the proposed approach is shown through numerical examples and compared to some recent methods

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

stochastic stability of delayed neural networks with local impulsive effects in this paper the stability problem is studied for a class of stochastic neural networks nns with local impulsive effects the impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants hence the impulses here can encompass several typical impulses in nns the aim of this paper is to derive stability criteria such that stochastic nns with local impulsive effects are exponentially stable in mean square by means of the mathematical induction method several easy to check conditions are obtained to ensure the mean square stability of nns three examples are given to show the effectiveness of the proposed stability criterion

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

on the linear static output feedback problem the annihilating polynomial approach abstract one of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback we are given a linear dynamical system defined through w a w b u y c w the problem is to find if it exists a feedback u k y such that the matrix a b k c has all its eigenvalues in the complex left half plane and if such a feedback does not exist to prove that it does not substantial progress has not been made on the computational aspect of the solution to this problem in this paper we consider instead which annihilating polynomials can a matrix of the form a b k c possess we give a simple solution to this problem when the system has either a single input or a single output for the multi input multi output case we use these ideas to characterize the annihilating polynomials when k has rank one and suggest possible computational solutions for general k we also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

on a conjecture of helleseth regarding pairs of binary m sequences binary m sequences are maximal length sequences generated by shift registers of length m that are employed in navigation radar and spread spectrum communication it is well known that given a pair of distinct m sequences the crosscorrelation function must take on at least three values this correspondence addresses a conjecture made by helleseth in 1976 that if m is a power of 2 then there are no pairs of binary m sequences with a 3 valued crosscorrelation function this conjecture is proved under the assumption that the three correlation values are symmetric about 1

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

improved results on h model reduction for continuous time linear systems over finite frequency ranges this paper revisits the h model reduction problem for continuous time linear systems over finite frequency ranges given an asymptotically stable system our goal is to find a stable reduced order system in such a way that the error of the transfer functions between the original system and the reduced order one is bounded over a finite frequency range by virtue of the generalized kalman yakubovich popov gkyp lemma we first establish necessary and sufficient characterizations for this problem in terms of linear matrix inequalities lmis for the low and mid frequency cases through introducing a non conservative multiplier and resorting to the projection lemma the reduced order system matrices are decoupled with the matrix variables from the gkyp lemma then by introducing a new diagonal matrix variable and based on congruence transformation the reduced order system matrices are further decoupled with the matrix variable induced by the projection lemma and can be parameterized by a new matrix variable the results are extended to the high frequency case without the use of projection lemma to reduce the conservatism moreover an iterative convex optimization algorithm is developed to solve the conditions finally we demonstrate via numerical examples that our method can achieve much smaller approximation error than existing results

stability analysis of linear systems under state and rate saturations in this paper we provide a stability analysis for linear systems which have simultaneous saturations in the states and their rates dynamics the stability analysis is conducted via a formulation based on the polytopic representations of two saturation functions state and rate saturation functions sufficient conditions to guarantee local and global asymptotical stability of such systems are derived furthermore using the invariance analysis we estimate the domain of attraction of the system when it is locally asymptotically stable the stability conditions are formulated as an iterative lmi ilmi algorithm finally numerical examples are presented to validate the proposed method

a note on functional observability in this note we propose an alternative to characterize the functional observability for linear systems the main feature is that we obtain a necessary and sufficient condition for the existence of a stable multi functional observer of a time invariant linear system the proof of this condition is constructive and it leads to design a stable observer via a new procedure neither based on the solution of a sylvester equation nor on the use of canonical state space forms

an ilmi approach to robust static output feedback sliding mode control this paper proposes a systematic methodology for designing robust static output feedback sliding mode control sofsmc for a class of systems with mismatched uncertainties this methodology consists of two parts one is a new sufficient and necessary condition for the existence problem in terms of two matrix inequalities the other is a direct solving method using the iterative linear matrix inequality ilmi technique the main advantages of this method are that only original system parameters are involved without any extra coordinate changes and that appealing to solving the static output feedback stabilization sofs problem is no longer required in addition the ilmi algorithm includes an optimal part to avoid high control efforts a numerical example also demonstrates the efficacy of the proposed approach