Study On Some Problems Of Discrete-time Stohastic Systems With Multiplicative Noises

As is known to us,stability,H_? and H₂/H_? are important concepts for stochastic systems in control theory and are applied in the engineering field successfully.This paper is concerned with the finite horizon mixed H₂/H_? control problem for systems with infinite Markov jump parameters and multiplicative noise. Besides, we consider LQ control for stochastic systems with ?- and??,?? - stability degree for continuous-time case, and with ? - stability degree for discrete-time case.For discrete-time time-varying systems with infinite Markov jump parameters and multiplicative noise, a stochastic bounded real lemma ?SBRL? is presented. Further, a sufficient and necessary condition for the existence of the mixed H₂/H_? control problem is supplied by the solvability of four coupled difference matrix-valued recursions ?CDMRs?.Also, the version of linear matrix inequalities ?LMIs? to the control problem is obtained.What's more, by using the approach of the non-zero-sum Nash game, it is successfully to unify H₂,H_? and H₂/H_? control and get the optimal strategy. Finally, the paper is concerned with the state feedback linear quadratic control with regional pole placement constraints for stochastic systems subject to multiplicative noises. By the Lagrange multiplier method,necessary conditions are obtained for the optimal controller satisfying ?- and??, ?? - stability of continuous-time case, and ? - stability of discrete-time case, respectively.