| Singular systems have found many successful applications in practice.The magnitude of input and output signals that actuators and sensors deliver is inevitably limited by physical constrains in practical control systems.If the effects of input or output saturation are not taken into account when we design a controller,peculiar and pernicious consequences may occur.This thesis considers the stabilization problem for singular systems with input saturation,output saturation or sandwich saturation.The main results are listed as follows:First,we address the controller synthesis problem for discrete-time singular systems subject to both input saturation and Lipschitz nonlinear perturbation.A sufficient condition for the existence and uniqueness of a state feedback controller is presented,which guarantees the admissibility of the closed-loop systems.The largest contractively invariant set can be determined by solving an optimization problem with convex constraints.Second,the stabilization problem for linear singular systems with saturated outputs is considered.Such systems are assumed to be regular and impulse-free.Thus,they can be reduced to the state-space form with direct feedthrough term.The necessity of considering the direct feedthrough term is clarified.Then we present a constructive design strategy to achieve globally asymptotic stability of the closed-loop systems by output feedback.The controller is continuous during the interval we drive a specific output component out of saturation in order to handle the direct feedthrough term.And the parameters to be designed for the controller have close relationship with the transfer function and direct feedthrough matrix.Finally,we deal with the stabilization problem for singular sandwich systems with saturation nonlinearity.Under the regularity and non-impulsiveness assumptions,the singular subsystems are reduced to the state-space systems with direct feedthrough.We use detectors to determine whether the saturation is active or not.Then a constructive design strategy is presented to stabilize the open-loop sytems by output feedback.The controller design strategy is divided into three stages.It is continuous in each stage to avoid discontinuous output. |
