Addressing stability challenges in linear descriptor systems: A unified approach to robust control

Abstract

This paper focuses on studying the robust stability of linear descriptor systems with perturbations in the state matrix under rank-deficient and unmatched conditions. In fact, there are three main steps in this study. The first is constructing an equivalent optimal control to design a robust control. The second step is to solve the Riccati equation to find the optimal control solution. The third step is to implement the cost function of the equivalent optimal control to define the candidate Lyapunov function in order to verify the stability conditions. The proposed control method is verified through simulations. Our results demonstrate that the proposed approach can guarantee robust stability under uncertain and perturbed conditions.

Keywords

• Descriptor system
• Optimal control
• Robust control
• Uncertainty
• Unmatched condition
• Stability