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Recursive algorithm for mixed $$H_2/H_{\infty}$$ control problem of singularly perturbed systems. (English) Zbl 1080.93586
Summary: We study the mixed $$H_{2}/H_{\infty }$$ control problem for infinite-horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of parametrized cross-coupled algebraic Riccati equations with a small positive parameter epsilon. Firstly, we solve the parametrized cross-coupled algebraic Riccati equations using a L yapunov iteration approach. Sufficient conditions are provided such that the proposed L yapunov iterations converge to a positive semidefinite solution. Secondly, we propose a new algorithm, which combines Lyapunov iterations and recursive techniques together, to solve the parametrized cross-coupled algebraic Riccati equations. The new algorithm ensures that the solution of the parametrized cross-coupled algebraic Riccati equations converges to a positive semidefinite solution with the rate of convergence of $$O(\varepsilon^{k})$$. As another important feature of this paper, our method is applicable to both standard and non-standard singularly perturbed systems.

##### MSC:
 93-XX Systems theory; control
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