Abstract
AbstractThis paper investigates the optimization problem for a class of switched interconnected positive linear systems (SIPLSs), of which each subsystem is composed of several positive interconnected components. Both the continuous‐time and periodic sampling control schemes are considered. Combining with the characteristics of the interconnection and positivity, a novel class of multiple co‐positive Lyapunov functions is constructed. Based on the multiple Lyapunov functions method, a state‐dependent switching law with a dwell time constraint is introduced so that the state is continuously evaluated after the dwell time. Furthermore, the designed switching law is extended to a new sample‐based scenario where the state is periodically evaluated after the dwell time. In both cases, suitable cost functions are selected to estimate the performance of the SIPLSs, and the upper bounds are calculated. Finally, numerical examples are considered to illustrate the effectiveness of the presented results.
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