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Stabilization of uncertain systems with norm bounded uncertainty - a control Lyapunov function approach. (English) Zbl 0682.93050
Summary: A robust stabilization problem in a state-space setting is treated. It is assumed that the states are available for feedback. Using a fixed Lyapunov function approach (quadratic stability) it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state-feedback controller. As a consequence, it is shown that the existence of a quadratically stabilizing nonlinear time-varying dynamic state-feedback controller implies the existence of a quadratically stabilizing memoryless linear time-invariant state-feedback compensator.

93D15Stabilization of systems by feedback
93B35Sensitivity (robustness) of control systems
93C05Linear control systems
93C15Control systems governed by ODE
93C35Multivariable systems, multidimensional control systems
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