∞ guaranteed cost control for uncertain continuous-time linear systems

This paper deals with the _∞ guaranteed cost control problems for continuous-time uncertain systems. It consist of the determination of a stabilizing state feedback gain which imposes on all possible closed-loop models an _∞ -norm upper bound γ > 0. Assuming that the uncertain domain is convex-bounded and the uncertain system is quadratic-stabilizable with γ disturbance attenuation, it is shown how to determine, by means of a convex programming problem, the global minimum of γ. As a particular and important case, for precisely known linear systems, the last problem reduces to the classical _∞ optimal control problem. The results follow from the definition of a special parameter space on which the above-mentioned problems are convex.