2013/10/24 by Yue Wang, Vijay Gupta, Panos J. Antsaklis · 53 citations
Engineering · Mathematics · #Adaptive Control of Nonlinear Systems #Affine transformation #Bounded function #Computer science #Control (management) #Control and Stability of Dynamical Systems #Control theory (sociology) #Discrete time and continuous time #Dynamics and Control of Mechanical Systems #Engineering #Function (biology) #Mathematical analysis #Mathematics #Mode (computer interface) #Nonlinear system #Passivity #Physics
paper · doi:10.1109/tac.2013.2287074
published in IEEE Transactions on Automatic Control 59(3), 692-702 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2013/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
This paper analyzes the passivity and feedback passivity of discrete-time-switched nonlinear systems with passive and nonpassive modes that are affine in the control input. When a nonpassive mode is active, the increase in storage function is not necessarily bounded by the energy supplied to the switched system at every time step. Therefore, a switched system with at least one nonpassive mode is defined to be nonpassive in the classical passivity theory. In this paper, we propose a framework to analyze the passivity of such switched systems in a more general sense. We consider switched nonlinear systems which are affine in the control input and may consist of passive, feedback passive modes, and modes which cannot be rendered passive using feedback. In the proposed framework, we prove that a switched nonlinear system is locally feedback passive if and only if its zero dynamics are locally passive. A lower bound on the ratio of total activation time between (feedback) passive and nonfeedback passive modes is obtained to guarantee passive zero dynamics. Finally, we prove that two important properties of classical passivity still hold for the proposed passivity definition, that is: 1) output feedback control can be used to stabilize the switched system, and 2) parallel and negative feedback interconnections of two such passive systems are also passive.