H₂/H_? Control For Discrete-Time Stochastic Delay Systems

In the field of stochastic control,time-delay systems is one of the important research objects and has a wide range of practical applications.The analysis and synthesis of time-delay systems have been paid more attention by many experts and scholars.The influence of delay for different dynamic systems is also different.it is the main cause of system instability.In the study of dynamic systems,the control problem with time delay is often regarded as one of the most difficult problem.In this paper,we study the finite horizon mixed H2/H? control problems for discrete time-delay systems with infinite Markov jumps.The main contents and innovations are as follows:(1)The stability and stabilization of stochastic time-delay control systems are discussed by introducing the definition of operator spectrum,and then the time-delay systems are transformed into stochastic systems without time delay by variable substitution.(2)When the hybrid control problem of discrete time delay systems with infinite Markov jump is studied,the bounded real Lemma of stochastic time delay systems is given and proved,and the definition of control problems of stochastic systems is further given.The equivalent conditions for the existence of the solution are given.(3)The maximum theorem of discrete-time stochastic systems with time delay is studied.firstly,some conditions are given,on the basis of which the Hamilton function is established,and the maximum principle of stochastic systems with time delay is given and proved.On this basis,the stochastic control problem is solved.