Abstract: In order to solve the H_∞ control problem for a class of discrete singular systems with markov parameters, a design method based on the memoryless state feedback controller of mode-jumping is proposed. By transforming the solvability of the determinant equation into the relationgship between the eigenvalue of the matrix and zero, the problem of regularity is converted to the magnitude of the maximum eigenvalue, and the causality is guaranteed in terms of linear transformation and the block matrix. By using the constructed Lyapunov function and linear matrix inequalities, a sufficient condition that the systems be admissible is given and proved, and a sub-optimal design approach is presented. The controller is designed and the prescribed H_∞ performance condition is satisfied. Simulation results demonstrate that the proposed method is valid and that the system has strong restraint ability against disturbance.

Key words: discrete singular system, admissible, H_∞ control, linear matrix inequalities