Persistent Dwell-Time Switched Nonlinear Systems: Variation Paradigm and Gauge Design

• Published in: IEEE transactions on automatic control Vol. 55; no. 2; pp. 321 - 337
• Main Authors: HAN, Thanh-Trung, SHUZHI SAM GE, TONG HENG LEE
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Adaptive control; Applied sciences; Asymptotic properties; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Design engineering; Dynamical systems; Dynamics; Exact sciences and technology; Gages; Gain; gauge design; gauge Lyapunov function; Gauges; Information technology; Intelligent systems; Lyapunov method; Nonlinear dynamics; Nonlinear systems; Output feedback; output feedback control; Switched systems; switching-uniform control; Timing; Uncertainty; unmeasured dynamics; State feedback; gauge design; Non linear control; Feedback regulation; Control synthesis; gauge Lyapunov function; Adaptive control; Modeling; Time variation; Hybrid system; Time varying system; switched systems; switching-uniform control; output feedback control; Switching time; unmeasured dynamics; Multimodel control; Stopping time; Non linear system; Timed system; Closed feedback; Instability; Asymptotic approximation; Timing; State dependence; Output feedback; Lyapunov function
• ISSN: 0018-9286; 1558-2523; 2334-3303; 1558-2523
• DOI: 10.1109/TAC.2009.2034927

Asymptotic gain and adaptive control are studied for persistent dwell-time switched systems. Ultimate variations of auxiliary functions are considered for existence of asymptotic gain and a gauge design is introduced for switching-uniform adaptive control by partial state feedback and output feedback of switched systems subject to unmeasured dynamics and persistent dwell-time switching. The usage of the controlled dynamics as a gauge for the instability mode of the unmeasured dynamics makes it possible to design a control rendering the evolution of the overall system interchangeably driven by the stable modes of the controlled and unmeasured dynamics. Unmeasured-state dependent control gains are dealt with and unknown time-varying parameters are attenuated via asymptotic gain. Verification of asymptotic gain conditions is based on the relation between dissipation rates of unmeasured dynamics and timing characterizations ¿ p and T p of switching sequences.