Cambridge University Engineering Department Publications Database · 1989 · 103 citations · 0 references
Natural SciencesMathematicsSystems EngineeringDifferential EquationsDynamical SystemsSystems ModelingControl Of Dynamical SystemsControl SystemsControl TheoryController DesignStability TheoryTransfer FunctionsClassical Control TheoryClosed-loop Transfer FunctionsH-infinity ControlLqg ControlSpectral RadiusSpectral Radius AnalysisStability Analysis Of Linear SystemsTransfer Function Analysis
Simple state-space formulas are derived for all controllers solving the standard H(infinity) problem of finding, for a given number gamma greater than 0, all controllers such that the H(infinity) norm of the closed-loop transfer function is (strictly) less than gamma. It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma squared. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive stable free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e., H2) theory. A standard H2 solution is developed in parallel.