Decentralized control of impulsive interconnected switched positive time-delay systems under MDMDT switching

The paper addresses the issue of decentralized control with positivity constraint for impulsive interconnected switched positive systems (IISPSs) with mixed time-varying delays coexisting in the state term and the interconnection term under mode-dependent minimum dwell time (MDMDT) switching. Firstly, a positivity criterion of IISPSs is given from the aspect of sufficiency and necessity. Next, through adopting a new discretized linear copositive Lyapunov-Krasovskii functional approach, a sufficient stability criterion of IISPSs under MDMDT constraint is presented. Then, utilizing the method of matrix decomposition, for the mode-dependent controller gains, a valid decentralized controller design scheme in the mode-dependent piece-wise form with formulated linear programming (LP) condition is given for IISPSs under MDMDT constraint. Furthermore, the proposed decentralized control design can degenerate into the one for the case that mixed delay does not lie in IISPSs. At last, three examples are presented to verify the validity of decentralized control design.