## Exact decomposition of linear singularly perturbed $$H^ \infty$$-optimal control problem.(English)Zbl 0864.93041

The singularly perturbed $$H^\infty$$-optimal control problem under perfect state measurements, for both finite and infinite horizons, is considered. The exact decomposition of the full-order Riccati equations to the reduced-order pure-slow and pure-fast equations is obtained.
As a result, the $$H^\infty$$-optimum performance and suboptimal controllers can be exactly determined from these reduced-order equations. The suggested decomposition allows the development of effective algorithms of high-order accuracy.

### MSC:

 93B36 $$H^\infty$$-control 93C70 Time-scale analysis and singular perturbations in control/observation systems 93C05 Linear systems in control theory 93C73 Perturbations in control/observation systems
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### References:

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