C.E. de Souza

Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach

This paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time-delay. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state-space model. We develop methods for robust stability analysis and robust stabilization. The proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities.

H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback

The article concerns linear systems which are subject to both time-varying norm-bounded parameter uncertainty and exogenous disturbance. It addresses the robust H/sub infinity / control problem of designing a linear dynamic output feedback controller such that the closed-loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties. It is shown that such a problem is equivalent to a scaled H/sub infinity / control problem. >

Robust Kalman filtering for uncertain discrete-time systems

This paper is concerned with the problem of a Kalman filter design for uncertain discrete-time systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties. Furthermore, the guaranteed cost can be optimized by appropriately searching a scaling design parameter. >

Mode-Independent

This note addresses the problem of Hinfin filtering for continuous-time linear systems with Markovian jumping parameters. The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant Hinfin filter for systems where the jumping parameter is not accessible. The cases where the transition rate matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust Hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed filter designs are given in terms of linear matrix inequalities

{\cal H}_{\infty}

This note deals with robust stability and control of uncertain discrete-time linear systems with Markovian jumping parameters. Systems with polytopic-type parameter uncertainty in either the state-space model matrices, or in the transition probability matrix of the Markov process, are considered. This note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty. The design of both mode-dependent and mode-independent control laws is addressed. The proposed methods are given in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the derived results.

Filters for Markovian Jump Linear Systems

This paper deals with the robust minimum variance filtering problem for linear systems subject to norm-bounded parameter uncertainty in both the state and the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty. Two methods for designing robust filters are investigated. The first one deals with constant parameter uncertainty and focuses on the design of steady-state filters that yield an upper bound to the worst-case asymptotic error variance. This bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system, and it can be made tighter if a tight bound on the latter power spectrum can be obtained. The second method allows for time-varying parameter uncertainty and for general time-varying systems and is more systematic. We develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems.

Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems

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.

Robust minimum variance filtering

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

A necessary and sufficient condition for output feedback stabilizability

Until recently, it was believed that a necessary and sufficient condition for convergence of the Riccati difference equation of optimal filtering was that the system be both delectable and stabilizable. Recently, it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular. The present paper generalizes these results in several directions. First, properties of the algebraic Riccati equation are established for the case of singular state transition matrix. Second, several assumptions previously imposed in establishing convergence of the Riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability, weakening the conditions on the initial covariance, and allowing the state transition matrix to be singular. Third, results on the convergence and properties of the Riccati equations are expressed as both necessary and sufficient conditions, whereas previous results were only sufficient. These extensions mean that the results have wider applicability, including fixed-lag smoothing problems and filtering for systems with time delays. The implications of the results in the dual problem of optimal control are also studied.

Robust exponential stability of uncertain systems with time-varying delays

The problem of /spl Hscr//sub /spl infin// filtering for continuous-time linear systems with time-delayed measurement is investigated. The authors develop a methodology for designing linear filters which ensure a prescribed bound on the /spl Lscr//sub 2/-induced gain from the noise signals to the estimation error. Filtering problems for time varying systems over a finite-horizon, as well as stationary infinite-horizon filtering for time-invariant systems, are tackled. In the finite-horizon case, our estimation procedure entails an overdesign that stems from the last d seconds of the time interval [0,T], where d is the delay length. This overdesign becomes smaller as T increases, and it vanishes in the infinite-horizon case.