Groupe d’études et de recherche en analyse des décisions

# Mixed $$H_2 / H_\infty$$ Stochastic Control Problem

## Mohammad Dikko S. Aliyu et El-Kébir Boukas

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.

, 22 pages