Dissipativity-based static output feedback stabilization of dynamical systems

Abstract

This dissertation deals with the static output feedback control problem for continuous-time dynamical systems. Different strategies are proposed to stabilize three distinct classes of systems, namely the classes of linear time-invariant systems, linear parameter varying systems, and input saturated nonlinear systems, all considering uncertainties in the system model. The notion of strict QSR-dissipativity, also known as a necessary and sufficient condition for static output feedback stabilizability under certain circumstances, is applied to formulate new sufficient conditions in the form of linear matrix inequalities. In the case of uncertain linear systems, the proposed strategy considers more realistic models by including uncertainty in the system matrices. Moreover, a minimum bound for the decay rate of the system is a closed-loop performance constraint. In the linear parameter varying case, both uncertainties and external inputs are considered. Thus, the strategy suggests stabilization with the L2-gain performance criterion. In this case, it is considered a differential-algebraic representation that allows dealing with the broad class of systems whose matrices present rational or polynomial dependence on the parameters. Finally, uncertain saturated nonlinear systems are contemplated, which characterizes more realistic models by considering at the same time nonlinearities in the system model and the saturating actuator condition. In this case, the proposed strategy also transforms the system into a differential-algebraic representation allowing the system to present rational or polynomial dependence on the state and uncertain parameters. A generalized sector condition is used to deal with the saturation on the input, and rational Lyapunov functions (which are more generic than quadratic ones) are considered to obtain less conservative results compared to the recent literature. Furthermore, a recently developed iterative algorithm based on linear matrix inequalities is applied to compute the feedback gain matrices simultaneously to the minimization of an objective function. While the objective function is to minimize the L2 gain in the strategy for linear time-varying systems, in the approach for nonlinear ones, the objective function is the maximization of the region of attraction. For all cases, numerical examples are provided to highlight the effectiveness of the proposed strategies.