Finite-Time Robust Guaranteed Cost Control for Continuous-Time Singular Systems with Nonlinear Perturbation

This note investigates the finite-time control problem for continuous-time singular system with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipchitz constraint. The definition of finite-time robust control for singular system with nonlinear perturbation is firstly presented. Then a sufficient condition for the existence and uniqueness of solution to the singular system is presented. Third, a sufficient condition of finite-time guaranteed cost controller is presented in terms of linear matrix inequality via generalized Lyapunov function approach. Finally, the effectiveness of the developed approach for singular systems is illustrated by numerical example.