Finding the optimal H∞ controller for stochastic Markovian jumping systems by using parallel Kleinman iteration algorithm

Two computation iterative algorithm are studied to solve the coupled game algebraic Riccati equation (CGARE) associated with the optimal H_∞ control problems for a class of Markovian jumping linear systems (MJLSs). The two iterative algorithms are based on the framework of Kleinman iteration algorithm. At first, the direct parallel Kleinman iteration algorithm is proposed and the convergence of the iterative algorithm is established. Then, we introduce a more general iterative algorithm (called generalized parallel Kleinman iteration algorithm) with four different cases. Finally, a numerical example has been provided to demonstrate the effectiveness of the proposed algorithms.