H2 dynamic control for periodic Markov jump systems with repeated scalar nonlinearities

This paper investigates the H
₂
control problem for a class of periodic Markov jump systems with repeated scalar nonlinearities. Under the assumption on the nonlinear function and the framework of positive definite diagonally dominant Lyapunov function method, a sufficient condition is given to ensure the stochastic stability of the closed loop system with a prescribed H
₂
performance index. By the periodic property, the proposed infinite dimension problem is then transformed into a finite one. A new linearization method is employed to cast the proposed condition into a solvable convex problem. The minimum H
₂
performance index can be computed by standard optimization technique. Finally a numerical example is presented to illustrate the validness of the results obtained in this paper.