Robust Guaranteed Cost Output-Feedback Gain-Scheduled Controller Design

Abstract

In the paper a new robust guaranteed cost output-feedback gain-scheduled PID controller design technique is presented for affine linear parameter-varying systems under polytopic model uncertainty, with the assumption that the scheduled parameters are affected with absolute uncertainty. The proposed centralized or decentralized method is based on the Bellman-Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The robust stability and performance conditions are translated to an optimization problem subject to bilinear matrix inequalities, which can be solved or further linearized. As the main result, the suggested stability and performance conditions without any restrictions on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples.