Robust control of dynamic systems with time-varying uncertainties

Various classes of controllers for dynamic systems with time-varying uncertainties are discussed. All the controllers are designed based on Lyapunov or Lyapunov-like function approach. The time-varying uncertainty is assumed to be unknown but bounded by a prescribed set. No other restrictions on the rate of change of uncertainty are imposed. No statistical information regarding the uncertainty is utilized and the controlled system performance is guaranteed in a deterministic sense.; First, a complete computer-aided algorithm for the design of estimated state feedback linear controller for uncertain systems with linear nominal parts is introduced. Necessary and sufficient conditions for quadratic stabilizability are utilized to formulate the control. The controller is designed by a two level optimization process.; Second, it is shown that feedback linearization technique together with a saturation type nonlinear controller can render a class of uncertain nonlinear systems practical stable. Both input-state and input-output feedback linearization methods are addressed. In either case, matched cases and mismatched cases are both investigated.; Next, a composite control for linear two-time-scale systems is introduced. This control utilizes both linear and nonlinear control designs developed earlier. The design procedure starts with the construction of a linear controller for the slow dynamics of the system. A saturation type controller for the fast dynamics of the system is then constructed. This controller also takes into account the effects of slow controller. The true controller is a combination of these two partial controllers.; Fourth, the design of decentralized controllers for a class of uncertain interconnected nonlinear systems is considered. The nominal system is assumed to be feedback equivalent to a controllable-like canonical form. Feedback linearization technique is incorporated with a Lyapunov function based decentralized robust controller to guarantee the practical stability of the whole system.