Finite-time Control For Singular Markovian Jump Systems With Uncertainties In The Difference Matrices

Since the 70s of the last century,the theory of singular system has gradually developed into one of the most important branches of control theory.With its powerful application background,the singular system attracts the attention of many scholars at home and abroad.Compared with the standard state-space systems,the singularity of the difference(derivative)matrices of singular systems is a source of its distinguishing structural features and special characteristics.However,the difference(derivative)matrices of a singular system,which,just as the other matrices in state and input,is subject to possible perturbations due to the fact that existence of many uncertain factors in practical systems.At the same time,compared with the traditional control system,in view of changes has more complex structure and parameters,Markovian jump system can better describe the actual physical model.Therefore,how to design controller to eliminate or reduce the impact of uncertainty on system is of great practical value in singular Markovian jump system with uncertainties in the difference matrices.In this paper,the stability analysis,finite-time control and sliding mode control of singular Markovian jump systems with uncertainties in difference matrices are discussed by means of linear matrix inequalities.The main contents of this paper are summarized as follows:1.Robust finite-time control for singular discrete-time Markovian jump systems with uncertainties in the difference matrices.Two kinds of uncertain singular discrete-time Markovian jump systems with left-singular and right-singular matrices are considered.The sufficient conditions for robust finite time stability of the system and the design method of state feedback controller are given by using the augmented technology of the system.2.Robust finite-time control of singular discrete-time time-varying delays Markovian jump systems with uncertainties in the difference matrices.In the partly unknown transition probabilities under the conditions for the singular time-varying delay Markovian jump system,by using the free weight matrix method and the Lyapunov stability theory,a sufficient condition for the open-loop system to be robust finite time stability is given,and the state feedback controller is designed to ensure that the closed loop system is finite time stable.In order to facilitate the calculation,all the conditions are given in terms of strict linear matrix inequality.Finally,the simulation example of the system is given,and it is proved that the robust finite time controller is feasible and effective.3.Robust sliding mode control for singular discrete-time time-varying delays Markovian jump systems with uncertainties in the difference matrices and partially unknown transition probability.For the singular discrete time-varying delay Markovian jump system with uncertainties of the difference matrices,a sufficient condition for delay is given by using the free weight matrix method and the Lyapunov stability theory,which guarantees the stochastic stability of the system.In addition,a sliding mode controller is designed to ensure that the trajectory of the system is attracted to the sliding surface within a limited time.In order to reduce the difficulty of calculation,the sufficient conditions for the stability of the system are given in the form of linear matrix inequalities.Finally,the simulation results show that the sliding mode controller is feasible and effective.