Dwell-time-dependent asynchronous dissipative control for discrete-time switched positive systems with linear supply rates

This article investigates the issues of dissipativity analysis and synthesis of discrete-time switched positive systems, in the presence of asynchronous switching. A switching retard, between activation of positive subsystems and activation of candidate controllers, is taken into account. The dwell-time dependent linear copositive storage functions and linear supply rates are adopted to capture the property of dissipativity, where the state of each subsystem is required to stay in positive orthant. Sufficient conditions are also attained such that the closed-loop system with time-varying asynchronous state-feedback controllers maintains positivity and meets strict $(q,r)$-$\alpha$-dissipative performance. Furthermore, all derived criteria are presented in the form of linear vector inequalities. Finally, two examples including the compartmental model are offered to illustrate the validity of derived results.