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

optimal control of linear time varying systems via piecewise linear polynomial functions a linear time varying optimal control system with a quadratic performance index is solved by using piecewise linear polynomial functions only a small number of basis functions are needed to produce a satisfactory result and the outcome is much better than the solutions obtained by using walsh functions block pulse functions or taylor polynomial series owing to the available recursive formula the computational work is convenient and straightforward

new oscillation criteria for linear matrix hamiltonian systems abstract some new oscillation criteria are established for the matrix linear hamiltonian system x a t x b t y y c t x a t y under the hypothesis a t b t b t 0 and c t c t are n n real continuous matrix functions on the interval t 0 t 0 these results are sharper than some previous results even for self adjoint second order matrix differential systems

oscillation theorems for self adjoint matrix hamiltonian systems involving general means by use of monotone functionals and positive linear functionals a generalized riccati transformation and the general means technique some new oscillation criteria for the following self adjoint hamiltonian matrix system e x t a t x t b t y t y t c t x t a t y t are obtained the results obtained improve and complement that of kumari et al 2000 on kamenev type theorems moreover these results generalize and improve earlier results due to meng 2002 for e erbe et al 1993 meng et al 1998 and wang 2001 for p t x t q t x t 0 or its special cases and wong 2001 for the scalar system x t q t x t 0

robust detectability from the measurements plus state feedback stabilization imply semiglobal stabilization from the measurements we study the problem of stabilizing with large regions of attraction a general class of nonlinear system consisting of a linear nominal system plus uncertainties a similar result was given by the same author in previous works in this note we prove that what was referred in these works to as nonlinear coupling condition can be reformulated in the control design as a nonlinear rescaling of the lyapunov functions of the closed loop system plus the requirement for a suitably faster convergence of the state estimation error we obtain a paradigm very similar to the linear case for which if a couple of riccati like inequalities state feedback and observer design are satisfied then a measurement feedback stabilizing controller can be readily found examples are given for showing improvements over the existing literature

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

oscillation criteria for linear matrix hamiltonian systems abstract in this paper we present oscillation criteria in terms of the coefficient functions for the matrix linear hamiltonian system u a x u b x v v c x u a x v under the hypothesis h a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i a a these criteria generalize earlier results due to etgen and pawlowski 1976 erbe qingkai kong and shigui ruan 1993 and fanwei meng jizhong wang and zhaowen zheng 1998 for the system p x u q x u 0 or its special cases

application of chebyshev polynomials to the optimal control of time varying linear systems the operational matrix of backward integration for the shifted chebyshev polynomials is introduced in this study the general expression of the shifted chebyshev polynomial approximation for any two arbitrary functions is also presented a linear time varying optimal control system with a quadratic performance measure is solved by using the shifted chebyshev polynomials only a small number of chebyshev polynomials is needed to produce an excellent result and the outcome is much better than the solution obtained by using the block pulse function so computer memory capacity and computing time can be saved considerably

weighted means and oscillation conditions for second order matrix differential equations on considere le systeme d equations differentielles d ordre 2 p t y t q t y t 0 pour t 0 ou p et q sont des matrices symetriques n n reelles sur 0 et y un vecteur colonne on suppose que p t est definie positive pour tout t tel que p t 1 on donne des conditions d oscillations

oscillation theorems for self adjoint matrix hamiltonian systems by using generalized riccati technique linear positive functional and the weighted averages technique some new oscillation criteria for self adjoint hamiltonian matrix system e u x a x u x b x v x v x c x u x a x v x are obtained these results generalize and improve earlier results due to kumari and umamaheswaram 9 for e parhi and praharaj 12 etgen and pawlowski 6 for p x u x q x u x 0 or its special cases and coles 3 for the scalar system y x q x y x 0

oscillation of self adjoint linear matrix hamiltonian systems abstract by means of monotone functionals defined on suitable matrix spaces and new methods oscillation criteria for self adjoint linear hamiltonian matrix system of the form x x a x x x b x y x y x c x x x a x y x are obtained there results are sharper than some previous results even for self adjoint second order matrix differential systems in particular our theorems are generalizations and improvements of many existing results including those obtained by sun j math anal appl 279 2003 651 658

dwell time controllers for stochastic systems with switching markov chain we study the problem of feedback stabilization of a family of nonlinear stochastic systems with switching mechanism modeled by a markov chain we introduce a novel notion of stability under switching which guarantees a given probability that the trajectories of the system hit some target set in finite time and remain thereinafter our main contribution is to prove that if the expectation of the time between two consecutive switching dwell time is sufficiently large then the system is stable under switching with guaranteed probability we illustrate this methodology by constructing measurement feedback controllers for a wide class of stochastic nonlinear systems

on stability of randomly switched nonlinear systems this note is concerned with stability analysis and stabilization of randomly switched systems these systems may be regarded as piecewise deterministic stochastic systems the discrete switches are triggered by a stochastic process which is independent of the state of the system and between two consecutive switching instants the dynamics are deterministic our results provide sufficient conditions for almost sure stability and stability in the mean using lyapunov based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds this slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants this condition is shown to hold for switching signals coming from the states of finite dimensional continuous time markov chains our results therefore hold for markovian jump systems in particular for systems with control inputs we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems

riccati techniques and variational principles in oscillation theory for linear systems on etablit des conditions suffisantes pour que toutes les solutions soient oscillatoires on utilise les techniques de riccati et les principes variationnels

analysis and optimal control of time varying linear systems via taylor series the taylor series is used for the analysis of time varying linear systems with the introduction of the product matrix of the taylor polynomial vector and its transpose for the solution of the optimal control problem the operational matrix of backward integration for the taylor series is introduced in this way the state transition matrix of optimal control of linear systems with quadratic performance index may be integrated approximately via taylor series the results obtained indicate an excellent agreement with the exact solution for a small number of terms

oscillation theorems for certain second order self adjoint matrix differential systems abstract by means of generalized averaging pair technique and riccati transformation method oscillation criteria for self adjoint differential matrix system of the form r t p t x t p t p t x t q t f x t g x t 0 are obtained this paper generalizes and improves the existing results including those obtained by yang 2002 li and agarwal 2000 and rogovchenko 1999

notions of observability for uncertain linear systems with structured uncertainty this paper introduces a notion of observability for a class of uncertain linear systems with structured uncertainty in the uncertain systems under consideration the uncertainty is described by averaged integral quadratic constraints in order to define a notion of observability for uncertain linear systems the paper introduces a robust observability function which extends the usual definition of the observability gramian to the case of uncertain systems using this observability function a corresponding unobservable cone is defined and an uncertain system is said to be robustly observable if this cone contains only the origin the paper presents an algorithm for finding the robust observability function and corresponding unobservable cone this algorithm involves solving a parameterized riccati differential equation

analysis and optimal control of time varying linear systems via shifted legendre polynomials this paper extends the application of shifted legendre polynomial expansion to time varying systems the extension is achieved through representing the product of two shifted legendre series in a new shifted legendre series with this treatment of the product of two time functions the operational properties of the shifted legendre polynomials are fully applied to the analysis and optimal control of time varying linear systems with quadratic performance index

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching