Asymptotic expansions for game-theoretic Riccati equations and stabilization with disturbance attenuation for singularly perturbed systems. (English) Zbl 0784.93040

Summary: If the systems to be controlled are singularly perturbed, then the Riccati equations which appear in \(H_ \infty\) problems are difficult to solve due to the presence of the small parameter. The present paper describes and validates asymptotic expansions, showing how they may be used in \(H_ \infty\) control. Furthermore, we construct a composite controller based on the solution of slow and fast problems, which guarantees a desired achievable performance level for the full-order plant as \(\varepsilon\) approaches zero.


93C15 Control/observation systems governed by ordinary differential equations
93C73 Perturbations in control/observation systems
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