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This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach. Index Terms--Domain of attraction, nonlinear systems, parameter-dependent Lyapunov function, polynomial systems, stability, uncertain systems.

This note addresses the design of robust [H.sub.2] filters for linear systems with a state-space model subject to time-varying uncertain parameters with limited variation. The uncertain parameters and their rate of variation are assumed to belong to a given convex-bounded polyhedral domain. A method based on a parameter-dependent Lyapunov function is proposed for designing a linear stationary asymptotically stable filter with a guaranteed average error variance, irrespective of the uncertain parameters. The proposed design is formulated in terms of linear matrix inequalities. Index Terms--Convex-bounded uncertainties, parameter-dependent Lyapunov function, robust [H.sub.2] filtering, time-varying parameters, uncertain systems.

This note addresses the problem of [H.sub.[infinity] 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 [H.sub.[infinity] 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 [H.sub.[infinity] 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. Index Terms--[H.sub.[infinity] filtering, Markovian jump linear systems, mode-independent filter, robust filtering.

This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result. Index Terms--Markov jump systems, nonlinear systems, stochastic Lyapunov functions, uncertainty.

The problem of robust H(infinity) filtering for linear discrete-time state-spaces models with uncertain time-varying parameters are addressed. This design reduces the overdesign encountered in the existing linear matrix inequality approach of robust H(infinity) filtering through a parameter-independent Lyapunov function.

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. Index Terms--Discrete-time systems, Markovian jump linear systems, robust stability, robust stabilization.

The problem of finite-horizon Kalman filtering is examined, for systems using a norm-bounded uncertain block. A new technique is proposed for robust Kalman filter design.

Research describing robust H(infinite) filtering for linear discrete time systems subject to uncertain parameters is presented. In particular system state-space models with multiple time delays in the state variables are investigated.

Research describing the design of a stable linear filter with asymptotic stability irrespective of time delays and uncertainties is presented. The methodology is established in terms of linear matrix inequalities.

This paper is concerned with the problem of [H.sub.[infinity]] control for a class of nonlinear systems. The system under consideration is assumed to be globally asymptotically stable with a known Lyapunov function. Based on this Lyapunov function and using the notion of dissipativeness, a state feedback controller is designed which renders the closed-loop system globally asymptotically stable with a prescribed bound on the [L.sup.2]-gain from the disturbance input to the controlled output. The proposed controller design method is based on the explicit construction of a Lyapunov function for the closed-loop system, which represents a significant advantage over existing methods. Index Terms - [H.sub.[infinity]] control, [L.sub.2]-gain, nonlinear systems, state feedback.

This paper 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. Index Terms - Exponential stability, robust stability, time-varying delay, uncertain systems.

A method of designing robust filters involves constant parameter uncertainty and follows the configuration of steady-state filters, giving an upper bound to asymptotic error variance. This bound varies with the upper limit of the power spectrum density of specific signals in the system. Another method follows the uncertainty rule of time-varying parameters. These two methods are applicable for fabricating filters with optimum upper bound to estimate the error variance in the areas of finite and infinite horizon filtering.

This note deals with the H(sub infinity) state estimation problem for linear periodic systems. The question addressed is the design of an unbiased linear periodic and asymptotically stable estimator that achieves a prescribed H(sub infinity) performance on infinite horizon. Necessary and sufficient conditions for the existence of a periodic estimator have been derived. Asymptotic properties of the finite horizon estimation problem when the time-horizon tends to infinity are also investigated.