Robust control for uncertain singular systems with disk pole constraints

In this paper, the robust control problems are discussed for uncertain continuous-time and discrete-time singular systems with disk pole constraints. First of all, the uncertain singular system without control input matrix perturbation is discussed. The concept of generalized quadratic d-stability is introduced for uncertain singular systems. A method of designing the state feedback controller is presented based on some matrix inequalities and the generalized Riccati equation, so that the singular closed-loop system is regular, impulse-free or causal as well as satisfying that all finite closed-loop poles are located within a preassigned circular region for all admissible parameter uncertainties. Secondly, the uncertain singular system with control input matrix perturbation is investigated. The condition for the existence of desired robust state feedback gain matrix is obtained and the analytical expression of the desired robust state feedback gain matrix is also proposed. Illustrative examples are given to demonstrate the effectiveness of the design method proposed in this paper.