Analysis and synthesis of interconnected SISO positive systems with switching

This paper addresses the analysis and synthesis of interconnected systems constructed from SISO positive subsystems and a nonnegative interconnection matrix. We focus on the case where the interconnection matrix switches over a finite set of given nonnegative matrices. By analyzing the existence of a first integral, we clarify a condition under which the state of the interconnected system, starting from any nonnegative initial state, becomes nonnegative and bounded under arbitrary switching. By extending this result, we establish a linear-programming-based method to synthesize the interconnection matrices to achieve a switching formation control of multi-agent positive systems.