Stability Analysis And Finite-time Energy-to-peak Control For Markov Jump Systems With Input Time Delay

In the actual system,due to changes in the working environment or failure of system components,the state of the system will often jump,and if it is not considered reasonably,it may cause a decline in system performance.As an important method to describe stochastic systems,Markov jump system can conveniently describe many systems in practical applications.Therefore,a large number of scholars solve the problem of analysis and control of practical systems by studying Markov jump systems.In addition,due to the time consumption of signal transmission and processing,time delay is often unavoidable in practical systems,and the existence of time delay will also lead to poor system performance or even system damage.Therefore,it is of great theoretical significance and application value to study the stability analysis and control methods of Markov jump time-delay systems.In this paper,the linear inequality technique is used to discuss the stability analysis,finite-time energy-to-peak control and H-infinity control of several classes of Markov jump systems with time-delay.(1)The control problems of signal transmission time delay and quantization error in networked control system are discussed.The networked control system is described as a variable time delay system,and based on candidate functions and the related mathematical operations,a theorem is obtained to keep H-infinity stable for systems with variable time delay.At the same time,the solutions of signal quantization error are given on this basis.(2)Based on the linear matrix inequality technique,the analysis and control problem of state constraint for Markov jump systems with input delays are discussed,and the controller design condition of H-infinity stability under state constraint is given.and this condition is extended to the uncertainty discussed in the case of stability.The obtained theorems are less conservative than some existing results.Finally,three simulation examples are used to verify the effectiveness of the theorems.(3)The finite-time energy-to-peak control problem of Markovian jump time-delay systems is studied.Based on Newton-Leibniz formula,the state space with multiple distributed delay terms is used to describe the system with pure time delay.At the same time,according to the linear matrix inequality technique,the sufficient conditions for the finite-time energy-to-peak stability of Markov jump systems with pure time delay are obtained.On this basis,the theorems are extended to Markov jump systems with regular time delay,and then the stability theorems and controller design methods are obtained under the two kinds of time delays.The theorems obtained in this paper are verified by relevant numerical examples.The experimental results show that the control method in this paper can not only effectively guarantee the stability of the Markov jump system under different time delays,but also has certain advantages compared with other control methods.