Robust stabilization of systems with multiplicative perturbations

In this paper we discuss robust stabilization of systems subject to multiplicative perturbations. For a given ball of perturbed systems around our nominal model, we find necessary and sufficient conditions under which we can find a controller which stabilizes each system in this ball. We give an explicit formula for a number \gamma* with the property: the radius of the ball is less than \gamma* if and only if there exists one controller which stabilizes all systems in the ball. Therefore \gamma* is the best we can do. Moreover, under an extra assumption and if they exist, we derive an explicit formula for a controller which stabilizes all systems in the given ball. Keywords: Roo control, algebraic Riccati equation, quadratic matrix inequality.