Multiple Lyapunov Functions Analysis Approach for Discrete-Time-Switched Piecewise-Affine Systems Under Dwell-Time Constraints

• Published in: IEEE transactions on automatic control Vol. 65; no. 5; pp. 2177 - 2184
• Main Authors: Zhu, Yanzheng, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Asymptotic stability; Control stability; Control systems; Discrete time systems; Dwell-time switching; Feedback control; Liapunov functions; Linear systems; Lyapunov methods; Mathematical analysis; multiple Lyapunov functions (MLFs); Nonlinear systems; Partitions; piecewise-affine (PWA) approximation; Quadratic forms; Stability analysis; stabilization; Subsystems; switched nonlinear systems; Switches; Switching
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2938302

In this technical note, the asymptotic stability analysis and state-feedback control design are investigated for a class of discrete-time switched nonlinear systems via the smooth approximation technique. The modal dwell-time switching property is considered to constrain switchings between nonlinear subsystems. A kind of autonomous switchings, i.e., state-partition-dependent switching, is introduced within each approximated piecewise-affine (PWA) subsystem. Combining with the state partition information, the novel asymptotic stability conditions with less conservatism are derived for the induced switched PWA systems with dual switching mechanism based on the approach of multiple Lyapunov functions in piecewise quadratic form. Then, the design of PWA state-feedback controllers is implemented. The effectiveness of the obtained theoretical results is demonstrated by a numerical example.