Dissipativity for Discrete-Time Switched Positive Delay Systems: A Dwell-Time-Dependent Linear Copositive Storage Functional Method

Abstract

This article addresses the problems of dissipativity analysis and feedback dissipativity of discrete-time switched positive systems with time-varying delay. On the basis of the positivity property of the investigated system, the definition of linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(q,r)$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -dissipativity, utilizing the linear copositive storage functionals with linear supply rates, is first introduced. The switching among subsystems is orchestrated by a state-dependent switching policy that obeys prespecified dwell-time constraints. Second, in order to reduce the conservatism brought by the identical summation term functional for all positive subsystems, we propose a dwell-time-dependent linear copositive storage functionals involving summation terms which are diverse appearing in the functional. Then, less conservative criteria are developed to guarantee the system is strict <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(q,r)$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -dissipativity by resorting to the switching policy or the joint implementation of the switching policy and time-varying controllers for subsystems. Finally, the validity of the proposed techniques is illustrated through two examples, and the relationship among the minimum dwell time, performance index, and time-varying delay is also revealed.