Robust observer design for continuous-time and sampled-data nonlinear systems

Effective control and monitoring of a system requires sufficient frequent information on the essential internal variables of the system called states. Most techniques used in control design as well as virtually all problems of systems analysis assume that the state is available in real time. Unfortunately, the state is usually too expensive or even impossible to measure. The problem of determining or reconstructing the states from output (sensor) measurements is referred to as the observer design or state estimation problem.;The observer convergence via exact discrete-time model is proved. Then, for the nonlinear sampled-data systems, the practical convergence of the proposed observer in the absence of exact model which is quite often the case is shown using the Euler approximate discrete-time model.;Following the same approach, we also study an important open problem in the control theory, static output feedback stabilization (SOF). We propose new (SOF) solutions for a class of nonlinear systems with uncertainties in both strict LMIs and SDP frameworks.;For linear time-invariant systems observer design has a well established solution. Despite recent advances, nonlinear systems on the other hand, represent a difficult challenge and nonlinear state estimation is a problem that remains largely unsolved. In this research, we focus on the robust nonlinear observer design for nonlinear systems targeting systems with norm-bounded uncertainties. We formulate our design problems as linear matrix inequalities (LMIs) which are becoming a standard tool in control theory due to their exceptional mathematical strength and highly efficient numerical solvability. An H infinity observer design for Lipschitz nonlinear systems is proposed in the form of LMI optimization problem both in the continuous and discrete time domains. Besides having asymptotic convergence and guaranteed disturbance attenuation level, the proposed observer is robust against some nonlinear uncertainty as well as norm-bounded parametric uncertainty. The new LMI formulation allows optimizations both on the Hinfinity cost and nonlinear uncertainty robustness. Furthermore, a new approach of robust Hinfinity observer design for a class of Lipschitz nonlinear sampled-data systems is proposed in the form LMIs. As an additional feature, maximizing the admissible Lipschitz constant, the solution of the proposed LMI optimization problem guarantees robustness against some nonlinear uncertainty for which bound are derived through norm-wise and element-wise robustness analysis. In the continuous-time domain, the results are extended to nonlinear descriptor systems in the form of a semidefinite programming (SDP) problem and strict LMIs.