The conservatism reduction problem of dissipative dynamic output feedback (DOF) control for a class of average dwell time switched system is investigated via a multistep Lyapunov function (LF) approach. First, a larger dissipative region with guaranteed stability and specifically, smaller level can be achieved by increasing a predictive step N, which means the monotonic requirement of LF is relaxed. Then, based on the results of dissipative analysis, a robust dissipative DOF controller is further designed. Unlike the traditional method that introduces equality constraint to obtain numerical testable conditions with heuristic nature, a less conservative controller is designed, where the LF matrix is formulated without structural constraint.
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