With Markov Jumping Parameters Of The Discrete Time Delay Systems Of Non-fragile Control

Markovian jump linear systems have the advantage of better representing physical systems with abrupt variations. Therefore a lot of research has been focused on this class of systems. Time delays and parameter uncertainties always exist in manufacturing systems and telecommunication systems etc. They are frequently the sources of instability and performance degradation in many dynamic systems. On the other hand, fragility relates to the uncertainties in the implementation of a designed controller due to something wrong with hardware or software in practice. The resulting controllers with a certain degree of uncertainties will exhibit a poor performance margin. Thus the non-fragile control of discrete-time Markovian jump linear systems with time delay have come to play an important role in science and engineering applications.This dissertation investigates the problems of robust and non-fragile stabilization, robust and non-fragile H∞control, non-fragile guaranteed cost control and H∞guaranteed cost control for a class of discrete-time Markovian jump linear systems with time delay based on Lyapunov stability theory, linear matrix inequality (LMI) and free-weighting-matrix approach. The uncertainties exist both in the controlled system and the gains of the controller. The purpose of the robust and non-fragile stabilization is to design a memory state feedback controller with a different delay such that the closed-loop system is robust stochastically stable for all admissible norm-bounded uncertainties. As for the robust and non-fragile H∞control problem, in addition to the robust stochastic stability requirement, a prescribed H∞performance is required to be achieved. In the non-fragile guaranteed cost control problem, the controller guarantees the robust stochastic stability of the closed-loop system and the upper bound of quadratic performance. Furthermore, the non-fragile H∞guaranteed cost control problem is discussed. The closed-loop system is robust stochastically stable, satisfies a prescribed H∞performance level and the given quadratic cost function has an upper bound for all admissible uncertainties. In terms of a set of coupled linear matrix inequalities, delay-dependent sufficient conditions for the solvability of these problems are proposed respectively; the expressions of desired state feedback controllers are also given. Compared to existing literatures, these conditions have fewer variables and are easier to resolve. Numerical examples are provided to demonstrate the effectiveness of the proposed approaches.