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

Abstract

This paper is concerned with the problems of finite-time H 2 / H ∞ 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 mode-dependent parameter approach (MDPA) is adopted, to obtain some less conservative results for the existence of state feedback and observer-based feedback finite-time H 2 / H ∞ controllers. Compared with the common parameter approach, the advantages of MDPA are clearly shown. Moreover, H 2 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 H 2 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 H 2 and H ∞ performance indices. Finally, a detailed design example is given to illustrate the merits of the proposed results.