Optimal Sliding Mode Control for Linear Singualr System with Input and State Time-Delays

Abstract

Synthetic problem of variable structure control (VSC) for linear singular system with input and state time-delays is studied. Firstly, the original system with both input and state time-delays is written into a form without time-delay by a linear transformation. Secondly, the system without time-delay is decomposed into two low dimensional subsystems by a restricted system equivalent decomposed method. Thirdly, the quadratic performance index optimal control technique is introduced to design the optimal sliding mode for the restricted equivalent subsystems. By applying reaching law approach, the selected control law ensures that the solution trajectories of the system reach the switching manifold in finite time and have low chattering in the sliding motion. Finally, a simulation example is given to illustrate the feasibility and validity of the proposed method.