Publication record · 18.cifr/1989.doyle.h2-hinf-state-space

State-space solutions to standard H2 and H-infinity control problems

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J.C. Doyle (California Institute of Technology), K. Glover (University of Cambridge), P.P. Khargonekar (University of Minnesota), B.A. Francis (University of Toronto)

RAI18.cifr/1989.doyle.h2-hinf-state-space

IEEE Transactions on Automatic Control· 1989· doi:10.1109/9.29425

Explicit state-space formulas are derived for the standard H2 and H-infinity control problems. The solutions involve two algebraic Riccati equations and a spectral radius condition, providing a unified framework for robust controller synthesis that replaced earlier operator-theoretic approaches with numerically tractable algorithms.

H-infinity controlH2 controlalgebraic Riccati equationrobust controlstate-space synthesisoutput feedback

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Before this paper, H-infinity synthesis had no practical computational path for state-space plants. Engineers lacked a direct algorithm to produce robust controllers for real systems. This work gave a closed-form, software-implementable recipe: solve two AREs and check one spectral condition.

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Derived explicit state-space formulas for both H2 and H-infinity controllers via algebraic Riccati equations, replacing operator-theoretic methods with a finite-dimensional, numerically computable synthesis procedure. The H-infinity result showed feasibility is equivalent to two AREs having stabilizing solutions whose product satisfies a spectral radius bound.

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