Control of linear systems subject to constraints: Stabilization, output regulation and performance analysis

This thesis attempts to address design and analysis issues arising from linear systems with constraints. The emphasis is on design and analysis issues from external stability point of view, but the connected important problems of internal stabilization and output regulation are also treated by utilizing the methodologies developed in the course. The goal is to build a basic understanding of the behavior of linear systems with constraints under some appropriate designs. Following some previous work in the literature, we continue to address interesting problems on linear systems with different types of constraints, including stabilization with amplitude and rate constraints in the semi-global and global framework, output regulation with input constraints or state constraints in the semi-global and global framework, and the related performance issues when disturbance and uncertainty also appear in the system. A set of preliminary and fundamental results have been established in this dissertation.; For linear systems with input saturation and non-input-additive disturbance, we show that global asymptotic stabilization and global external L_p stabilization with finite-gain is impossible by using bounded control for general asymptotically null controllable systems. This result points us to a critical issue that the external stabilization of linear systems with input saturation is more delicate than expected, and needs a thorough study from new perspective. This consideration is justified by studying a simplified system including a double integrator with a saturated linear stabilizing control. We find that for such a system with non-input-additive disturbance, the L_P stability only holds for p ∈ [1, 2], but not for p ∈ (2, ∞).; Utilizing an operator based model for amplitude and rate constraints, we have developed output regulation schemes for systems with amplitude and rate saturation at the input, and systems with amplitude and rate constraints at both input and state. A main advantage of adopting the operator based constraint model is that most techniques and design methodologies developed so far for amplitude constraints can easily be extended to the constraints involving both amplitude and rate constraints. (Abstract shortened by UMI.)...