new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

switched nonlinear systems with state dependent dwell time the asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied the system switches among a family of integral input to state stable systems the time between two consecutive switchings is not less than a value d this dwell time d is allowed to take different values according to a function whose argument is the state of the system at the switching times we propose a dwell time function which depends on the comparison functions which characterize the integral input to state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with bounded energy the main feature of the analysis is that it does not rely on the property for the switching to stop in finite time the two important cases of locally exponentially stable and feedforward systems are analyzed in detail

the strict bounded real lemma in infinite dimensions abstract the strict bounded real lemma is generalized to an infinite dimensional setting this relates the existence of a stabilizing solution to a riccati equation to an h norm bound and to the existence of a solution to a riccati inequality

a small gain theorem for switched interconnected nonlinear systems and its applications a small gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems also a method exploiting an average dwell time and the small gain technique is proposed based on the small gain theorem this technical note investigates the problem of global stabilization of switched nonlinear systems in strict feedback form whose all zero dynamics are input to state stable iss or only some are iss and others are not a sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state feedback controllers for subsystems the result is also applied to a class of switched nonlinear network control systems

delay independent minimum dwell time for exponential stability of uncertain switched delay systems in this technical note the problem of delay independent minimum dwell time for exponential stability of uncertain switched delay systems is considered piecewise time varying lyapunov functionals functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time varying delays this type of delicately constructed lyapunov functionals functions can efficiently eliminate the jump phenomena of adjacent lyapunov functionals functions at switching times without imposing any restriction on the sizes of time delays by applying this type of lyapunov functionals functions it is shown that if each subsystem is delay independently exponentially stable then under some conditions there exists a delay independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time delays two numerical examples are provided to demonstrate the efficiency of the proposed approach

input to state stabilization of switched nonlinear systems this note derives some sufficient conditions to ensure that the whole switched nonlinear system is input to state stabilizable iss when each mode is iss both cases that the switchings of system modes coincide exactly and that they do not coincide with those of the corresponding controllers are considered for the latter a model based identification scheme is used to identify the system modes the proposed scheme can overcome the finite escape time that may happen in this case

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

controllability properties of perturbed distributed parameter systems abstract we analyse the action of perturbations on controllable distributed parameter systems we show that the most common controllability properties are not preserved under the action of perturbations whose norm is smaller than any prescribed tolerance v 0 in particular we show that small perturbations of the values of the coefficients of a system with delays can destroy the property of modal controllability finally a positive result which is important for application to the stabilization problem is presented

on the newtonkleinman method for strongly stabilizable infinite dimensional systems we consider the newtonkleinman method for strongly stabilizable infinite dimensional systems under certain assumptions the maximal self adjoint solution to the associated control algebraic riccati equation is constructed the constructed solution is also the maximal solution to the corresponding control algebraic riccati inequality

existence and comparison theorems for algebraic riccati equations for continuous and discrete time systems abstract we discuss two comparison theorems for algebraic riccati equations of the form xbr 1 b x x a br 1 c a br 1 c x q c r 1 c 0 simultaneously we give sufficient conditions to obtain the existence of the maximal hermitian solution of a riccati equation from the existence of a hermitian solution of a second riccati equation further similar results are given for discrete algebraic riccati equations

generalized riccati equations arising in stochastic games abstract we study a class of rational matrix differential equations that generalize the riccati differential equations the generalization involves replacing positive definite weighting matrices in the usual riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games both stochastic and deterministic the purpose of this paper is to prove some fundamental properties such as comparison monotonicity and existence theorems these properties are well known for classical riccati differential equations when certain matrices are assumed definite as applications we obtain conditions for the existence of solutions to the algebraic riccati equation and to equations with periodic coefficients

adaptive neural control for a class of switched nonlinear systems in this paper adaptive neural control is presented for a class of switched nonlinear systems with switching jumps and uncertainties in both system models and switching signals condition on limiting variation of the lyapunov function is given for input to state asymptotic stability of switched systems with switching jumps the control objective is achieved uniformly with respect to a class of switching signals the coupled difficulties from the discrepancy between control gains and switching jumps are overcome by discontinuous adaptive neural control combined with the classical adaptive control smooth approximations of the discontinuous controls are then presented for a systematic design procedure

stabilizing switching signals a transition from point wise to asymptotic conditions abstract characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature this article collects a multitude of stabilizing switching signals under an umbrella framework we achieve this in two steps firstly given a family of systems possibly containing unstable dynamics we propose a new and general class of stabilizing switching signals secondly we demonstrate that prior results based on both point wise and asymptotic characterizations follow our result this is the first attempt in the switched systems literature where these switching signals are unified under one banner

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

interval estimation for continuous time switched linear systems this paper deals with the design of interval observers for switched linear systems sls a class of hybrid systems under the assumption that the disturbances and the measurement noise are bounded upper and lower bounds for the state are calculated new conditions of cooperativity in discrete time instants are firstly proposed then some techniques for interval estimation are developed in continuous time it is shown that it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable via some change of coordinates under arbitrary switching sequences the performances of the developed techniques are illustrated through numerical examples

bibo stabilization of piecewise switched linear systems with delays and nonlinear perturbations this paper deals with bibo stabilization of piecewise switched linear systems in presence of delays and nonlinear perturbations based on piecewise quadratic lyapunov functional the main contribution of the paper is the derivation of sufficient conditions of bibo stabilization in the form of algebraic riccati matrix equation the robust quadratic stability for such system is also discussed a numerical example is given to illustrate the effectiveness of the theoretical results

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

nontrivial twisted sums of c 0 and c k abstract we obtain a new class of compact hausdorff spaces k for which c 0 can be nontrivially twisted with c k

comparison theorems for infinite dimensional riccati equations abstract comparison theorems are proved for the algebraic riccati equation in the framework of infinite dimensional hilbert spaces these theorems extend well known results for the finite dimensional case

a representation of all solutions of the control algebraic riccati equation for infinite dimensional systems we obtain a representation of all self adjoint solutions of the control algebraic riccati equation associated to the infinite dimensional state linear system a b c under the following assumptions a generates a c0 group the system is output stabilizable strongly detectable and the dual riccati equation has an invertible self adjoint non negative solution

bibo stabilization for system with multiple mixed delays and nonlinear perturbations the problem of bibo stabilization for multiple mixed time delayed control system with nonlinear perturbations is studied in this paper the new delay dependent bibo stabilization criteria are derived by the lyapunov functional and given in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such system is also discussed the work of this paper will extend the results of some references

quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays abstract this paper deals with the quadratic stability and linear state feedback and output feedback stabilization of switched delayed linear dynamic systems with in general a finite number of non commensurate constant internal point delays the results are obtained based on lyapunov s stability analysis via appropriate krasovsky lyapunov s functionals and the related stability study is performed to obtain both delay independent and delay dependent results it is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a in general non unique stabilizing switching law when the system is polytopic stable at some interior point of the polytope but with non necessarily stable parameterizations at the vertices defining the subsystems it is also proved that two subsystems individually parametrized in different polytopic type sets which are not quadratically stable might be stabilized by a in general non unique switching law provided that a convexity type condition is fulfilled at each existing pair of vertices one corresponding to each subsystem some extensions are provided for a typical class of neutral time delay systems

on input to state stability of stochastic nonlinear systems with markovian jumping parameters in this article the input to state stability iss properties of stochastic nonlinear systems with markovian jump parameters are considered firstly the notions of stochastic iss e t weighted integral iss in mean and in the pth mean are introduced then by the lyapunov like function method some corresponding criteria are provided lastly a simulation example is provided to illustrate the effectiveness of our results

homogeneous riccati equations versus quadratic inequalities it is proved that under certain hypotheses the existence of hermitian solutions of a homogenized algebraic riccati equation of continuous type is guaranteed if the corresponding quadratic inequality admits a hermitian solution both finite dimensional matrices and infinite dimensional hilbert space operators riccati equations are considered

impulsive stabilization of second order nonlinear delay differential systems modeling of many dynamic systems results in second order delay differential systems in this paper we prove that two kinds of delay systems without impulses can be stabilized by proper impulsive control respectively our results have improved and generated some of the known results found in the literature we also give an example to illustrate the obtained results

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

h sub 2 guaranteed cost control for singularly perturbed uncertain systems the h sub 2 guaranteed cost control problem for a singularly perturbed norm bounded uncertain system is addressed using the quadratic stabilizability framework after defining the corresponding slow and fast uncertain subsystems the set of quadratic stabilizing composite controls is characterized two riccati equations have to be solved one for the slow subsystem and the other for the fast subsystem choosing appropriately the weighting matrices it is shown how to pick up in the set of quadratic stabilizing composite controls a control minimizing an upper bound on the h sub 2 norm of a certain transfer matrix the case of the guaranteed cost control problem for the reduced system is also investigated

brief paper input to state stability and integral input to state stability of nonlinear impulsive systems with delays this paper is concerned with analyzing input to state stability iss and integral iss iiss for nonlinear impulsive systems with delays razumikhin type theorems are established which guarantee iss iiss for delayed impulsive systems with external input affecting both the continuous dynamics and the discrete dynamics it is shown that when the delayed continuous dynamics are iss iiss but the discrete dynamics governing the impulses are not the iss iiss property of the impulsive system can be retained if the length of the impulsive interval is large enough conversely when the delayed continuous dynamics are not iss iiss but the discrete dynamics governing the impulses are the impulsive system can achieve iss iiss if the sum of the length of the impulsive interval and the time delay is small enough in particular when one of the delayed continuous dynamics and the discrete dynamics are iss iiss and the others are stable for the zero input the impulsive system can keep iss iiss no matter how often the impulses occur our proposed results are evaluated using two illustrative examples to show their effectiveness

asymptotic h sub spl infin control of singularly perturbed systems with parametric uncertainties this paper deals with the problem of control of singularly perturbed linear continuous time systems the authors attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed h sub spl infin performance for the full order system are achieved the asymptotic behavior of the composite controller is studied which is independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small furthermore the problem of robust control for the above system with parameter uncertainty is also investigated

brief bibo stability integral l gain for second order systems with numerator dynamics it is shown that the most stressful bounded disturbance for linear stable second order systems with numerator dynamics is bang bang and can be realized in feedback form using a switch curve especially for the second order systems with a finite zero an explicit formula is given for the bounded input bounded output stability integral based on the time maximum disturbance switch curve this closed analytic form requires less computational effort and gives an intuitive feeling as to how the l gain will change with the free system parameters

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

extension operators and twisted sums of c0 and c k spaces abstract we investigate the following problem posed by cabello sanchez castillo kalton and yost let k be a nonmetrizable compact space does there exist a nontrivial twisted sum of c 0 and c k i e does there exist a banach space x containing a non complemented copy y of c 0 such that the quotient space x y is isomorphic to c k using additional set theoretic assumptions we give the first examples of compact spaces k providing a negative answer to this question we show that under martin s axiom and the negation of the continuum hypothesis if either k is the cantor cube 2 1 or k is a separable scattered compact space of height 3 and weight 1 then every twisted sum of c 0 and c k is trivial we also construct nontrivial twisted sums of c 0 and c k for k belonging to several classes of compacta our main tool is an investigation of pairs of compact spaces k l which do not admit an extension operator c k c l

the kalman yakubovich popov lemma for pritchard salamon systems in this paper we generalize the kalman yakubovich popov lemma to the pritchard salamon class of infinite dimensional systems i e systems determined by semigroups of operators on a hilbert space with unbounded input and output operators at the same time we prove a comparison theorem for riccati equations of the same class

stability and bifurcation analysis on a logistic model with discrete and distributed delays in this paper a logistic model with discrete and distributed delays is investigated we first consider the stability of the positive equilibrium and the existence of local hopf bifurcations in succession using the normal form theory and center manifold argument we derive the explicit formulas which determine the stability direction and other properties of bifurcating periodic solutions a numerical simulation for supporting the theoretical analysis is also given

twisted sums with c k spaces if x is a separable banach space we consider the existence of non trivial twisted sums 0 c k y x 0 where k 0 1 or for the case k 0 1 we show that there exists a twisted sum whose quotient map is strictly singular if and only if x contains no copy of 1 if k we prove an analogue of a theorem of johnson and zippin for k 0 1 by showing that all such twisted sums are trivial if x is the dual of a space with summable szlenk index e g x could be tsirelson s space a converse is established under the assumption that x has an unconditional finite dimensional decomposition we also give conditions for the existence of a twisted sum with c with strictly singular quotient map

uniform input to state stability for switched and time varying impulsive systems we provide a lyapunov function based method for establishing different types of uniform input to state stability iss for time varying impulsive systems the method generalizes to impulsive systems with inputs the well established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the lyapunov function on the system trajectories this reduction is performed in such a way that the resulting scalar system has no inputs novel sufficient conditions for iss are provided which generalize existing results for time invariant and time varying switched and nonswitched impulsive and nonimpulsive systems in several directions

output tracking control of nonlinear switched cascade systems using a variable structure control method this article is concerned with the output tracking control problem for a class of nonlinear switched cascade systems under some average dwell time based switching laws firstly stabilisation problem of this class of switched systems is considered then the result is extended to the output tracking control problem based on the variable structure control technique and the characteristic of the system the variable structure controllers and the average dwell time are designed the effectiveness of the proposed design approach is illustrated with simulation results

bibo stabilization of feedback control systems with time dependent delays abstract this paper investigates the bounded input bounded output bibo stability in a class of control system of nonlinear differential equations with time delay the proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear volterra integral equations

bibo stabilization of time delayed system with nonlinear perturbation time delayed control system with the nonlinear perturbation is considered novel bibo stabilization criteria are established by the lyapunov functional and formulated in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such systems is also discussed a numerical example is given to illustrate the effectiveness of our result

existence and global exponential stability of periodic solution for discrete time bam neural networks the discrete time analogues of bidirectional associative memory neural networks with periodic coefficients and distributed delays are formulated and studied and by using the continuation theorem of coincidence degree theory we derive the existence of periodic solution for the discrete time bam neural networks and by constructing a appropriate lyapunov type sequence we prove the global exponential stability of the periodic solution for the model it is shown that the discrete time analogues inherit the existence and global exponential stability of periodic solution for the continuous time bam neural networks an example is given to illustrate the effectiveness of the obtained results

multiple lyapunov functions based small gain theorems for switched interconnected nonlinear systems multiple lyapunov functions mlfs based small gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems which extend the small gain technique from its original non switched nonlinear version to a switched nonlinear version each low dimensional subsystem does not necessarily have the input to state stability iss property in the whole state space and it only has individual iss property in some subregions of the state space the novelty of this paper is that integral type mlfs and small gain techniques are utilized to establish some mlfs based small gain theorems for switched interconnected nonlinear systems which derive various stability results under some novel switching laws designed and construct integral type mlfs the small gain theorems proposed cover several recent results as special cases which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are iss or only some are iss and others are not finally two illustrative examples are presented to demonstrate the effectiveness of the results provided

isolated nonnegative solutions of infinite dimensional algebraic riccati equations abstract for an infinite dimensional continuous or discrete time linear system based on the study of the representation of nonnegative solutions of the algebraic riccati equation are we get some sufficient and necessary conditions for a nonnegative solution of are to be isolated in the set of all nonnegative solution of are with respect to the norm topology the strong operator topology and weak operator topology respectively

variation of the parameters formula and the problem of bibo for singular measure differential systems with impulse effect recently we first presented and studied singular measure differential systems with impulsive solutions some fundamental theory was established in the present paper with the help of the drazin inverse the variation of the parameters formula of singular measure differential systems is obtained as an application the problem of boundary input and boundary output bibo is investigated

stability bounds of singularity perturbed systems a necessary and sufficient condition is developed for computing the upper bound in sub 0 of the parasitic parameter in in a singularly perturbed system which ensures stability of such a system if 0

input to state stability and interconnections of discontinuous dynamical systems in this paper we will extend the input to state stability iss framework to continuous time discontinuous dynamical systems dds adopting piecewise smooth iss lyapunov functions the main motivation for investigating piecewise smooth iss lyapunov functions is the success of piecewise smooth lyapunov functions in the stability analysis of hybrid systems this paper proposes an extension of the well known filippov s solution concept that is appropriate for open systems so as to allow interconnections of dds it is proven that the existence of a piecewise smooth iss lyapunov function for a dds implies iss in addition a small gain iss interconnection theorem is derived for two dds that both admit a piecewise smooth iss lyapunov function this result is constructive in the sense that an explicit iss lyapunov function for the interconnected system is given it is shown how these results can be applied to construct piecewise quadratic iss lyapunov functions for piecewise linear systems including sliding motions via linear matrix inequalities

necessary and sufficient conditions for j spectral factorizations with a j lossless property for infinite dimensional systems in continuous and discrete time necessary and sufficient conditions for j spectral factorizations are given in terms of the existence of a self adjoint stabilizing solution of an appropriate riccati equation in infinite dimensions furthermore it is shown that a certain j lossless property holds if and only if the stabilizing solution to the riccati equation is nonnegative definite we prove these results first for the continuous time case and thereby derive analogous results for the discrete time case by means of a bilinear transformation of the complex plane

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

class kl estimates and input to state stability analysis of impulsive switched systems abstract in this paper we investigate input to state stability of impulsive switched systems the goal is to bridge two apparently different but both useful stability notions input to state stability and stability in terms of two measures in the hybrid systems setting based on two class kl function estimates and a comparison theorem for impulsive differential equations two sets of sufficient lyapunov type conditions for input to state stability in terms of two measures are obtained for impulsive switched systems these conditions exploit some nonlinear integral constraints in terms of generalized dwell time conditions to balance the continuous dynamics and impulsive dynamics so that input to state stability is achieved despite possible instability of individual continuous subsystems or destabilizing impulsive effects an illustrative example is presented together with numerical simulations to demonstrate the main results

robust adaptive fuzzy control of a class of uncertain switched nonlinear systems with mismatched uncertainties this paper studies the adaptive fuzzy control problem for a class of uncertain switched nonlinear systems with mismatched uncerta inties and external disturbances a new switched adaptive control technique for the problem studied is set up such that the considered switched systems can be stabilized under a class of switching signals characterized by the generalized average dwell time condition first the adaptive state feedback controller is designed based on tuning the estimations of the bounds on switching parameters instead of estimating the switching parameters directly next by using a switched observer to reconstruct the states of the system an output feedback controller is also presented in the design procedure fuzzy logic systems are used to approximate the unknown nonlinear functions to overcome the undesirable chattering phenomenon both control laws are developed using the continuous control strategy it is shown that both controllers can guarantee that all the signals in the resulting closed loop system are bounded finally two simulation examples are presented to demonstrate the effectiveness of the proposed control results

a survey of nonsymmetric riccati equations abstract we survey recent and also older results on nonsymmetric matrix riccati differential equations and in the time invariant case on the corresponding algebraic riccati equations in particular we cite various applications connected with matrix riccati equations

certainty equivalence implies detectability abstract it is shown that any stabilizing certainty equivalence control used within an adaptive control system causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator s output error e p for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend the fact that certainty equivalence implies detectability has been known for some time this has been shown to be so whenever the process model is linear and the controller and estimator models are also linear for every frozen value of p in this paper use is made of recently introduced concepts of input to state stability and detectability for nonlinear systems to prove that the same implication is valid in a more general nonlinear setting

linear state space systems in infinite dimensional space the role and characterization of joint stabilizability detectability several fundamental results from the theory of linear state space systems in finite dimensional space are extended to encompass a class of linear state space systems in infinite dimensional space the results treated are those pertaining to the relationship between input output and internal stability the problem of dynamic output feedback stabilization and the concept of joint stabilizability detectability a complete structural characterization of jointly stabilizable detectable systems is obtained the generalized theory applies to a large class of linear state space systems assuming only that i the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators ii the state space is hilbert space iii the input and output spaces are finite dimensional and iv the sensing and control operators are bounded general conclusions regarding the fundamental structure of control theoretic problems in infinite dimensional space can be drawn from these results

a kleinman newton construction of the maximal solution of the infinite dimensional control riccati equation abstract assuming only strong stabilizability we construct the maximal solution of the algebraic riccati equation as the strong limit of a kleinman newton sequence of bounded nonnegative operators as a corollary we obtain a comparison of the solutions of two algebraic riccati equations associated with different cost functions we show that the weaker strong stabilizability assumptions are satisfied by partial differential systems with collocated actuators and sensors so the results have potential applications to numerical approximations of such systems by means of a counterexample we illustrate that even if one assumes exponential stabilizability the kleinman newton construction may provide a solution to the riccati equation that is not strongly stabilizing

generalized h2 output feedback controller design for uncertain discrete time switched systems via switched lyapunov functions abstract this paper investigates the generalized h 2 control problem for a class of discrete time switched systems with uncertainties the uncertain system is modelled as a polytopic type with linear fractional uncertainty in the vertices by using switched lyapunov functions new linear matrix inequalities lmis characterizing the generalized h 2 performance for discrete time switched systems are obtained based on the result a generalized h 2 output feedback controller is developed for uncertain discrete time switched systems a numerical example is included to demonstrate the effectiveness of the proposed result

brief hysteresis based switching algorithms for supervisory control of uncertain systems we address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers we present a new hysteresis based switching logic designed specifically for this purpose and derive a bound on the number of switches produced by this logic on an arbitrary time interval the resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics

on banach spaces whose norm open sets are fσ sets in the weak topology we investigate non separable banach spaces whose norm open sets are countable unions of sets closed in the weak topology and a narrower class of banach spaces with a network for the norm topology which is discrete in the weak topology in particular we answer a question of arhangel skii exhibiting various examples of non separable function spaces c k with a discrete network for the pointwise topology and consistently we answer some questions of edgar and oncina concerning borel structures and kadec renormings in banach spaces

universal construction of feedback laws achieving iss and integral iss disturbance attenuation we study nonlinear systems with both control and disturbance inputs the main problem addressed in the paper is design of state feedback control laws that render the closed loop system integral input to state stable iiss with respect to the disturbances we introduce an appropriate concept of control lyapunov function iiss clf whose existence leads to an explicit construction of such a control law the same method applies to the problem of input to state stabilization converse results and techniques for generating iiss clfs are also discussed

spectral properties of finite dimensional perturbed linear semigroups abstract many interesting cauchy problems arising in applications can be treated as finite dimensional perturbations of relatively simple problems in most applications these perturbations take place via boundary conditions it is the aim of this paper to investigate such cauchy problems and especially the spectral properties of the corresponding generators some general results are obtained that unify several well known results for functional differential equations and age dependent population dynamics applications to control problems as well as some nonlinear generalizations will appear in forthcoming papers

absolute exponential stability and stabilization of switched nonlinear systems abstract this paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are metzler nonlinearity of the systems is constrained in a sector field which is bounded by two odd symmetric piecewise linear functions multiple lyapunov functions are introduced to deal with the stability of such nonlinear systems compared with some existing results obtained by the common lyapunov function approach in the literature the conservatism of our results is reduced all present conditions can be solved by linear programming furthermore the absolute exponential stabilization for the considered systems is designed by the state feedback and average dwell time switching strategy two examples are also given to illustrate the validity of the theoretical findings

bibo stability of linear switching systems in this paper we show that for linear switching systems of the form x sub n 1 a sub n x sub n u sub n 1 where the matrices a sub n are chosen arbitrarily from a given set of matrices bounded input bounded output stability implies uniform exponential stability

permanence of a discrete n species cooperation system with time delays and feedback controls in this paper a discrete n species cooperation system with time delays and feedback controls is proposed by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

noise to state stability of random switched systems and its applications noise to state stability of random switched systems is investigated in this technical note by the aid of fubini s formula the criteria on noise to state stability in the moment of random switched systems are established under a reasonable assumption of second order processes as applications the control problems of spring pendulum in random environment are researched in addition nonlinear filtering is considered to ensure noise to state stability of filter error switched systems

multiple model self tuning control for a class of nonlinear systems this study develops a novel nonlinear multiple model self tuning control method for a class of nonlinear discrete time systems an increment system model and a modified robust adaptive law are proposed to expand the application range thus eliminating the assumption that either the nonlinear term of the nonlinear system or its differential term is global bounded the nonlinear self tuning control method can address the situation wherein the nonlinear system is not subject to a globally uniformly asymptotically stable zero dynamics by incorporating the pole placement scheme a novel nonlinear control structure based on this scheme is presented to improve control precision stability and convergence can be confirmed when the proposed multiple model self tuning control method is applied furthermore simulation results demonstrate the effectiveness of the proposed method

time varying discrete riccati equation some monotonicity results abstract using a fre chet derivative based approach some monotonicity and comparison results concerning the solutions of the time varying discrete time riccati equation are obtained connections with the existence of the semistabilizing solution are made explicit as well

algebraic riccati equation and symplectic algebra questions of existence uniqueness and the parametric dependence of solutions of the algebraic riccati equation are considered the different criteria for the solubility of this equation are obtained with the help of symplectic algebra

a lyapunov based small gain theorem for interconnected switched systems abstract stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input to state stable non iss we show that providing the switching signals neither switch too frequently nor activate non iss subsystems for too long a small gain theorem can be used to conclude global asymptotic stability gas of the interconnected system for each switched system with the constraints on the switching signal being modeled by an auxiliary timer a correspondent hybrid system is defined to enable the construction of a hybrid iss lyapunov function apart from justifying the iss property of their corresponding switched systems these hybrid iss lyapunov functions are then combined to establish a lyapunov type small gain condition which guarantees that the interconnected system is globally asymptotically stable

sailing over three problems of koszmider abstract we discuss three problems of koszmider on the structure of the spaces of continuous functions on the stone compact k a generated by an almost disjoint family a of infinite subsets of we present a solution to two problems and develop previous results of marciszewski and pol answering the third one we will show in particular that assuming martin s axiom the space c k a is uniquely determined up to isomorphism by the cardinality of a whenever a c while there are 2 c nonisomorphic spaces c k a with a c we also investigate koszmider s problems in the context of the class of separable rosenthal compacta and indicate the meaning of our results in the language of twisted sums of c 0 and some c k spaces

persistence and attractivity in an n species ratio dependent predator prey system with distributed time delays an n species ratio dependent predator prey food chain model with distributed time delays is investigated it is shown that the system is permanent under some appropriate conditions and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the system