The Guaranteed Cost Control And H_∞Filtering Of The Singular Markov Jump System

Markov systems are widely applied in many practical systems, butonce the rigid constraint occurs in the system, its original way ofdescription will subject to the limitation. The singular Markov jumpsystems are better able to describe some practical systems with rigidconstraints and stochastic process. On the other hand, in order to meetthe demand for system robustness and performance indicators, as wellas to solve the problem of uncertain disturbance, we take the guaranteedcost control andH filtering problem into consideration.Mainly utilizing mode dependent Lyapunov function, this paperuses the method of convex optimization to analyze problems, and getsome：(1) When the transition rate matrix (TRM) is known exactly anduncertain, the existence conditions for the mode-independent guaranteed cost control of singular Markov jump systems with time delays are established in terms of LMIs. Numerical examples are used to demonstrate the correctness of the results.(2) For such general TRMs mentioned above, the robustH filteing problems of a class of singular Markov jump systems are considered respectively. The conditions of both mode-dependentand mode-independent filters are developed within LMI framework. At the same time, a numerical example is used to showthe effectiveness of the above proposed methods.(3) When the TRM can be designed beforehand, both problems ofguaranteed cost control andH control for singular Markov jumpsystems are considered. The availability of the proposed results is illustrated by some numerical examples.(4) By considering the properties of singular Markov jump systems, wedevelop a simulation platform for mode-dependent guaranteed costcontrol, where the three cases in terms of TRM known exactly,uncertain and to be designed are considered. This simulation platformwill make the study of this kind of systems easy and convenient.