Zi-Kuan Liu

Robust H∞ filtering for polytopic uncertain time-delay systems with Markov jumps☆

Abstract This paper considers the filtering problem of jump linear systems with multiple delays and convex polytopic uncertain parameters. Some LMI-based conditions for the extended dynamical system to be robust stochastically stable and the estimation error satisfies a given noise attenuation level are provided and two LMI-based filter design algorithms are developed. Two illustrative examples are worked out to show the usefulness of the theoretical results.

Brief Manufacturing systems with random breakdowns and deteriorating items

This paper deals with the inventory control problem for production system in which multiple part types are produced and the produced parts are supposed to be deteriorating with fixed rates. The capacity of the production system is assumed to be random and bounded. The inventory control problem is formulated as a stochastic optimization problem that falls into the framework of the optimization problem of the class of systems with Markovian jumps. The optimal production rates are characterized and a numerical example is worked out to show the validness of the theoretical results.

Stability and Stabilizability

This chapter is devoted to the study of the stability and the stabilizability of linear time invariant systems with time delay using the Lyapunov method and linear matrix inequality (see Appendix A). For this purpose, let us consider the following linear continuous-time system with time delay:

Jump linear System with Time-Delay: Stability, Stabilization, H ∞ Control and Their Robustness

\left\{ \begin{gathered} \dot x(t) = Ax(t) + \Sigma _{j = 1}^mx(t - {\tau _j}) + Bu(t) \hfill \\ y(t) = Cx(t) \hfill \\ x(t) = \phi (t),\;t \in [ - \overline \tau ,0), \hfill \\ \end{gathered} \right.

Robust H∞ and Guaranteed Cost Control for Jump Linear Systems with Time Delay

(3.1)

Robust Stability and Robust Stabilizability

Practical systems are always subject to exogenous disturbance input which can cause performances degradations. The tools we developed are unfortunately inefficient for eliminating the effect of the disturbance. One alternative is to use the Roocontrol, which entails searching for a controller that stabilizes the system, and at the same time assures disturbance rejection at a given level. The7-l oo control problem has received considerable attention and thus numerous achievements have been reported to the literature. In the linear time-invariant context, early7-1control theory emerged as a frequency domain design technique [83].

Deterministic Time Delay Systems

This chapter studies the class of uncertain jump linear system with random time-delay. The norm bounded uncertainty type is considered. LMI-based sufficient conditions for the robust stability, state feedback stabilization and H ∞ control are developed.

Nonlinear Stochastic Control Problem

This chapter deals with stability and stabilizability problems of the class of linear systems with Markov jumps and time delay. For this purpose, consider a hybrid system withNmodes, that isS ={1, 2, • • •, N}. Mode switching is assumed to be governed by a continuous-time Markov process {rtt > Of taking values in the state spaceSand having the following infinitesimal generator