Continuous Singular Systems With Reliable Linear Quadratic Optimal Control

This thesis investigates the problem of designing reliable linear-quadratic state-feedback control for time-invariant continuous linear singular systems.Base on the solutions to generalized algebraic Riccati equation,when the outage of actuators within a pre-specified set occur,we design a reliable linear-quadratic regulator,which guarantees the admissibility(stability) and performances bound of the closed-loop systems.Furthermore,based on the Hamiltonian matrix pencil technique,a necessary and sufficient condition for the existence of admissible solutions to a class of the generalized algebraic Riccati equation is obtained,and a representation of all such solutions is given.As a medium step,a representation of all invertibilizing solutions to a class of algebraic Riccati equations is derived.In addition,numerical algorithms corresponding to main conclusions are designed,which offer convenience for applications of these obtained conclusions.The effectiveness of these proposed approaches is shown by examples.