Stability Analysis And Performance Control Of Complex Singular Systems

With the progress of modern social science and technology,various fields such as aerospace,electric power and transportation have been developed rapidly,and a large number of practical complex systems have emerged in practical engineering.The research and analysis of complex systems are now an important task for researchers.Singular systems,Markov jump systems and time-delay systems are all typical complex systems.With the increasing demand for industrial production,a single system can no longer accurately describe the complexity of industrial production.Finite time stability,H_? control and time delay are typical problems of such complex systems.Therefore,the study on the finite time stability of singular systems and singular Markov jump time-delay systems is not only of great theoretical importance,but also of great practical significance.This paper mainly studies a class of singular systems.The main contents are as follows:The finite time bounded and transient H_? control problem for a class of continuous singular systems with external disturbances is discussed.Firstly,a kind of performance measure is introduced,which is to adjust the norm of output when the disturbance input and initial state are known.By finding the finite time bounded conditions of the system and combining the linear matrix inequality approach,we obtain the sufficient conditions that the singular system is finite time bounded and the performance measure is less than the specified scalar.On this basis,the existence theorem of state feedback controller is proposed based on linear matrix inequality.Finally,a numerical simulation example is given to verify the effectiveness of the proposed method.The admissibility analysis and control synthesis of a class of singular systems with Markov jump and time-delay are discussed.The first assumption is that the time-delay can be constant or time-varying.By means of augmented Lyapunov-Krasovskii functional and linear matrix inequality,sufficient admissible conditions for singular Markov jump systems with time-delays are obtained.Then,these conditions are extended to solve the design problem of static output feedback control,two sufficient conditions are established,and an algorithm for the design of static output feedback control is given.Finally,a numerical simulation example is given to demonstrate the effectiveness of the proposed method.