In this paper, the mixed
\(H_2 / H_\infty\) control problem for continuous-time Markovian jumping linear systems using state-feedback control is considered. A Nash game approach to this problem is presented, and necessary and sufficient conditions for the solvability of this problem are given in terms of a set of two coupled Riccati equations. For the finite-horizon problem, the Riccati equations can easily be integrated using standard numerical schemes, while for the infinite-horizon, the solutions can be obtained as the limiting values of the finite-horizon case. The robust control problem with norm-bounded uncertainties is also considered. A quadratic stabilization approach to this problem is developed. Sufficient conditions for the solvability of this problem are given. Finally, simulation results are presented to show the usefulness of the results.
Published January 1999 , 22 pages