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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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