Guaranteed level-gamma H-infinity control in uncertain linear systems via linear matrix inequalities

Abstract

In this paper, we solve guaranteed level-gamma H-infinity control problems in uncertain linear systems. In time-varying systems, we provide a time-varying nonlinear differential equation for these problems, which can be solved via differential equation solvers. In time invariant systems, we present linear matrix inequalities (LMIs), which allow us to overcome the limitations of the existing algebraic Riccati equation (ARE) formulations, where one can hardly find their solutions. Since LMI problems are always convex, one can solve them via convex optimization techniques, such as interior-point methods, and can easily solve them even if additional constraints are considered. As a result, we directly handle the optimal guaranteed-level H-infinity control problem as well as a guaranteed level-gamma H-infinity control problem with the maximal stability margin. Finally, we present size-reduced LMIs.