Analysis And Synthesis Of Singular Systems With Time Delay

Singular systems can better describe some practical systems than state-space ones. On the other hand, time delays are often encountered in many control systems, and lead to the instability and degradation in control performance of control systems. Meanwhile, much attention has been paid to Markovian jump systems due to the fact that they have important practical applications. Thus, the study on singular systems with time delay and singular Markovian jump systems with time delay is important both in theory and in practice, and is of great interest to lots of researchers.In terms of linear matrix inequality approach, the problems of stability analysis, H∞control,H∞filtering and l2-l∞filtering are studied for singular (Markovian jump) systems with time delay. The main contents obtained in this dissertation are as follows:1. The H∞control problem for singular systems with time delay is discussed in terms of linear matrix inequality approach. A delay-dependent sufficient condition is pre-sented to ensure the system to be admissible with a prescribed H∞performance index via an augmented Lyapunov functional. Based on the condition, the design method for the H∞state feedback controller is presented.2. The problem of delay-dependent H∞filtering is considered for singular systems with time-varying delay. A filter is designed to guarantee the filtering error system to be exponentially admissible with a prescribed H∞performance level. The design method of the filter is given, which is based on the strict linear matrix inequalities.3. The stability analysis problem is investigated for discrete-time singular systems with time-varying delay. In terms of linear matrix inequality approach, a delay-dependent sufficient condition is obtained to guarantee the system to be regular, causal and stable. The proposed result has less conservatism than the existing one. 4. The problem of delay-dependent H∞control is considered for singular Markovian jump systems with time delay. A delay-dependent sufficient condition is obtained to guarantee the system to be stochastically admissible with a prescribed H∞per-formance level in terms of free-weighting matrix method. Based on the condition, the design method of the desired H∞state feedback controller is given. Numerical examples show the less conservatism of the proposed methods.5. The problem of H∞filtering is considered for singular Markovian jump systems with time delay. A sufficient condition is obtained to guarantee the system to be stochasti-cally admissible with a prescribed H∞performance level in terms of Jensen integral inequality. The delay-independent and delay-dependent conditions are proposed for the exist of the mode-independent filter. The design method of the desired filter is also given. Numerical examples are given to demonstrate that the given results have less conservatism than the existing ones.6. The problem of l2-l∞filtering is considered for discrete-time singular Marko-vian jump systems with time-varying delays. In terms of delay partitioning method, a delay-dependent sufficient condition is obtained to guarantee the system to be stochastically admissible with a prescribed l2-l∞performance level. The condi-tion is given for the exist of the mode-independent filter, and the design method of the desired filter is also given.Finally, the conclusion and further research topics are given.