State, Disturbance And Control Depend On Random Discrete H₂/H_? Control Of Noise

In recent years,H₂/H_?control has become a hot topic in the research of control comprehension.Recent advances in the theory of discrete-time stochastic systems have led to a new understanding of the control problems of discrete-time stochastic systems.The design of the optimal mixed H₂/H_?control can be constructed by solving some stochastic algebraic equations and establishing an equivalent relationship between them.In this paper,the problem of controller design for discrete-time stochastic systems with state,interference and control depending on noise is studied in infinite time do-main and finite time domain respectively,and a condition for the existence of control is proposed.Under these conditions,the design problems of state feedback controller is transformed into the solution of four coupled Riccati matrix equations.Using the above method,this paper can also solve the linear quadratic Stackelberg game for discrete-time stochastic systems with multiple decision makers whose state and control depend on noise in infinite time domain.Based on the solvability of coupled stochastic algebraic equations,the necessary conditions for the existence of Stackelberg strategy set have been found.