Optimization of Linear Systems Subject to Bounded Exogenous Disturbances: The Invariant Ellipsoid Technique

This survey covers a variety of results associated with control of systems subjected to arbitrary bounded exogenous disturbances. The method of invariant ellipsoids reduces the design of optimal controllers to finding the smallest invariant ellipsoid of the closed-loop dynamical system. The main tool of this approach is the linear matrix inequality technique. This simple yet versatile approach has high potential in extensions and generalizations; it is equally applicable to both the continuous and discrete time versions of the problems.