## 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.

### MSC:

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

### Keywords:

Riccati equations; singular perturbed systems
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### References:

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