Stabilization, observation, tracking and disturbance rejection for uncertain/nonlinear and time-varying systems.

摘要

In the first part of this study, we consider the problem of designing observers, stabilizing state and observer based output feedback controllers for a general class of nonlinear systems. The nonlinearities for this general class are described in terms of a quadratic inequality. First, analysis results are obtained. Basic Lyapunov stability theory is used to derive analysis results for quadratic stability of these systems. The controller and observer design procedures are established which involve solution of linear matrix inequalities (LMI's).; In the second part of this study, we consider uncertain/nonlinear systems subject to unknown constant disturbance inputs. We wish to design state feedback controllers which ensure that the system output asymptotically tracks a specified constant reference signal and all states are bounded. Our main result reduces the original problem to a stabilization problem for an associated augmented system which we call the "derivative augmented system". This system describes the dynamics of the derivative of an augmented state.; Then, we study the same problem by using a different approach. In this case, the dynamics between any two trajectories of an augmented system is considered. The stabilization of this dynamics leads to the desired tracking results. We obtain state and output feedback PI controllers to achieve this objective. The design procedures involve solution of LMI's.; In the third part, we apply the same controller structure on tracking problems where disturbance and reference signals have bounded derivatives. It is shown that tracking can be achieved with a bound on the tracking error, which is determined by the bound on the derivatives of disturbance and reference signals. It is also shown that the state vector and control input stay bounded if the disturbance and reference signals are bounded.