Stability of discontinuous retarded functional differential equations with applications

• Published in: IEEE transactions on automatic control Vol. 50; no. 8; pp. 1090 - 1105
• Main Authors: Ye Sun, Michel, A.N., Guisheng Zhai
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic stability; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Difference equations; Differential equations; differential-difference equations; discontinuous dynamical systems (DDS); Discrete event systems; Exact sciences and technology; exponential stability; Extraterrestrial measurements; hybrid systems; Integrodifferential equations; Lyapunov method; Lyapunov stability; Partial differential equations; retarded functional differential equations; Stability analysis; Sun; Switched systems; systems with delays; systems with delays; Multimodel control; Discontinuous; Differential equation; Functional equation; differential-difference equations; Delay system; retarded functional differential equations; Dynamical system; Difference equation; Exponential stability; discontinuous dynamical systems (DDS); Switching; Hybrid system; Asymptotic stability; hybrid systems; switched systems; Lyapunov stability; Switching system; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.852563

We present Lyapunov stability results, including converse theorems, for a class of discontinuous dynamical systems (DDS) determined by the solutions of retarded functional differential equations. We demonstrate the applicability of these results in the analysis of several specific important classes of DDS determined by functional differential equations and differential-difference equations.