Robust stability and stabilization conditions for uncertain switched positive systems under mode-dependent dwell-time constraints

The article addresses the problems of robust stability and stabilization in exponential sense for uncertain switched positive systems (SPSs) under mode-dependent dwell-time constraints including mode-dependent constant dwell time (MDCDT) constraint, mode-dependent minimum dwell time (MDMDT) constraint, and mode-dependent ranged dwell time (MDRDT) constraint. At first, the mixed time-varying delay case is studied, and sufficient conditions of robust stability and stabilization in exponential sense are provided for uncertain SPSs with MDMDT, MDCDT, and MDRDT constraints, respectively. Next, the robust stability and stabilization issues are also studied for SPSs in delay-free case. With mode-dependent dwell-time constraints, a new discretized linear copositive Lyapunov-Krasovskii functional technique is introduced in this article. Meanwhile, for some specific situations, the proposed conditions of robust stability and stabilization can be degenerated into the ones for SPSs in mode-independent dwell-time constraint case and in non-uncertainty case, respectively. At last, we give five examples to explain the importance and effectiveness of the results.