Convex optimization based dual gain observer design for Lipschitz nonlinear systems

International audienceThis paper deals with observer design for nonlinear Lipschitz systems via Linear Matrix Inequalities~(LMIs). Based on some recent work on the LPV approach, less conservative results are provided. A unified state observer that covers different classes of systems, namely linear systems, LPV systems with known and bounded parameters, and nonlinear Lipschitz systems. This observer leads to more general and less conservative sufficient conditions. To obtain LMIs, algorithms are proposed to design, a priori, some suitable observer parameters that enhance the feasibility of the LMIs. Interesting guidelines and techniques are proposed to reduce the number of LMIs of the classical LPV approach, decrease the effect of huge values of Lipschitz constant, which is the weakness of the standard LMI approaches