Analysis and control of switched linear systems via modified Lyapunov–Metzler inequalities

SUMMARY This paper addresses analysis and switching control problems of continuous/discrete‐time switched linear systems. A particular class of matrix inequalities, the so‐called Lyapunov–Metzler inequalities, will be modified to provide conditions for stability analysis and output feedback control synthesis under a relaxed min‐switching logic. The switching rule combined with switching output feedback controllers will be designed to stabilize the switched system and satisfy a prespecified gain performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in min‐switching based designs. The effectiveness of the proposed approach will be illustrated through numerical examples.