Finite-time H2/H? control for linear It? stochastic Markovian jump systems with Brownian motion and Poisson jumps

This paper is concerned with the problems of finite-time H2/Hoo control for linear stochastic Markovian jump systems (SMJSs) suffered from external disturbance and both Brownian motion and Poisson jumps. First, with the help of operator spectrum, a necessary and sufficient condition is given for the exact observability of SJMSs with Brownian motion and Poisson jumps, which is utilized to design observer-based controller. Second, a new differential inequality is constructed and the modedependent parameter approach (MDPA) is adopted, to obtain some less conservative results for the existence of state feedback and observer-based feedback finite-time H2/Hoo controllers. Compared with the common parameter approach, the advantages of MDPA are clearly shown. Moreover, H2 cost function under observer-based feedback proposed in this paper further considers the estimation errors on the basis of the states and estimations, which is more accurate than previous H2 cost function. Third, two new design algorithms are proposed. One is to search the ranges of some design parameters, and the other is to show the relationship between H2 and Hoo performance indices. Finally, a detailed design example is given to illustrate the merits of the proposed results.(c) 2022 Elsevier B.V. All rights reserved.