Stabilization And H_? Filtering For Nonhomogeneous Markov Jump Systems

Markov jump systems(MJSs)can describe the probabilities of jump between different modes,so they had attracted a lot attention in recent years.In this paper,the problems of control and filtering of nonhomogeneous MJSs were discussed.The difference between nonhomogeneous MJSs and homogeneous MJSs is that the transition probabilities of the nonhomogeneous is time-varying.The following three special nonhomogeneous MJSs were studied in theory,periodic nonhomogeneous discrete MJSs,higher-level nonhomogeneous discrete MJSs,and integral nonhomogeneous continuous MJSs with time-delay,the controllers or filters were designed.The main contributions of this paper are as follows:(1)Only in ideal situation,do accurately modeled system and precisely known transition probabilities exist,so uncertain periodic nonhomogeneous discrete-time MJSs with partly unknown transition probabilities were studied,and the periodic transition probabilities were described as polytope.By constructing Lyapunov functions,the stability of the considered periodic nonhomogeneous MJSs was analyzed.Next,a state-back controller for the considered system was designed,which ensured the closed-loop system was stochastically stable or had better stability performance.After that,for the considered system,to make the error system stochastically stable and satisfy H_?performance index,H_?filter was also designed.Periodic nonhomogeneous MJSs with partly unknown transition probabilities were studied in this paper.And in order to make the considered system satisfy the actual situation,uncertain system parameters were also introduced.(2)For nonhomogeneous discrete-time MJSs,to describe the variation of system transition probabilities,a higher-level Markov chain was introduced,and stochastic stability of the higher-level nonhomogeneous MJSs was analyzed via Lyapunov function.On the other hand,the asynchronous situation between considered system and controller was considered,and an asynchronous state-back controller was designed,which made sure the closed-loop system was stochastically stable and satisfied H_?performance index.Meanwhile,to denote the considered system mode is whether known or not,an independent Markov chain was introduced.In this part,the variation of transition probabilities of nonhomogeneous discrete-time MJSs was fully considered,and according to the actual production situations,an asynchronous controller was deigned,which was more valuable.(3)Taking the existence of time-delay in the actual production,the existed results about time-delay MJSs and the application of integral time-delay continuous systems into consideration,the results about integral time-delay were extended to nonhomogeneous continuous-time MJSs.By introducing some matrices and vectors,the stochastic stability was analyzed.And compared with existed results,the conservatism was reduced.In other words,a larger range of time-delay was obtained under the condition that considered system was stochastically stable.In this part,for nonhomogeneous continuous-time MJSs,integral time-delay was taken into account,and the conservatism was reduced via improving algorithm.