Controller Based Observer in Switched System with Norm Bounded Uncertainty

Problem statement: This study discusses the robust stabilization of norm bounded discrete switched systems. Approach: The proposed method is using the second Lyapunov approach and the poly-quadratic function concept. The stabilization conditions are written through linear matrix inequality relations. The control law is based on a static output feedback with the use of a switched observer. The synthesis conditions of the controller are written in the form of linear matrix inequalities difficult to resolve by current numerical solvers. That’s why relaxations are proposed to mitigate the pessimism of LMI conditions obtained. Results: The poly-quadratic Lyapunov approach provides a constructive way to tackle uncertainty in the switched framework. The feasibility is illustrated by the example of discrete uncertain switched systems. Conclusion: With these results, the study of stability can be achieved for arbitrary switching laws, state-dependent, time dependent or generated by a controller. However, the implementation of the control law is possible only if the switching status is well known in real time.