Stable controller design for linear systems

This paper is concerned with the problem of suboptimal stable mixed H₂/H_∞ control for linear time-invariant systems. The designed controllers are required to satisfy a prescribed H_∞ performance bound or a prescribed degree of stability. By reducing the stable controller synthesis problem to a multiobjective state feedback control problem for two different state models, sufficient conditions for the solvability of the considered problem are given in terms of solutions to algebraic Riccati equations and matrix inequalities. LMI-based iterative algorithms are developed to solve the stable controller synthesis problem. All of the proposed algorithms are shown to be convergent. An example is given to illustrate the proposed methods.