L2-L∞ control of singular jumping systems

In order to solve the L₂-L_infin control problem for a class of singular system 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 relationship between the eigenvalue of matrix and zero, the problem of regular was converted to the magnitude of the maximum eigenvalue, and the causal was guaranteed in terms of block matrix. By using the constructed Lyapunov function and linear matrix inequalities, a sufficient condition that the systems were admissible was given and proved, and a sub-optimal design approach is presented. The controller was designed and the peak of controlled output signals is restricted under a selected level while the energy of externed input signals is bounded. Finally, the simulation shows the effectiveness of the result.