Strict Lyapunov functions for time-varying systems

Uniformly asymptotically stable periodic time-varying systems for which is known a Lyapunov function with a derivative along the trajectories non-positive and negative definite in the state variable on non-empty open intervals of the time are considered. For these systems, strict Lyapunov functions are constructed.

[1]  D. Aeyels,et al.  A new asymptotic stability criterion for nonlinear time-variant differential equations , 1998, IEEE Trans. Autom. Control..

[2]  Dirk Aeyels,et al.  New criteria for exponential and uniform asymptotic stability of nonlinear time-variant differential equations , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[3]  L. Praly,et al.  Adding an integration and global asymptotic stabilization of feedforward systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[4]  L. Praly,et al.  Asymptotic tracking of a state reference for systems with a feedforward structure , 1997, 1997 European Control Conference (ECC).

[5]  J. P. Lasalle.  Stability theory for ordinary differential equations. , 1968 .

[6]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[7]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[8]  JiangZhong-Ping,et al.  Tracking control of mobile robots , 1997 .

[9]  K. Narendra,et al.  Persistent excitation in adaptive systems , 1987 .

[10]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[11]  A. Teel.  Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem , 1998, IEEE Trans. Autom. Control..

[12]  Frédéric Mazenc,et al.  Lyapunov stability analysis for nonlinear delay systems , 2001 .

[13]  Frédéric Mazenc.  Interconnected nonlinear systems, local and global stabilization , 1998 .

[14]  M. Jankovic.  Control Lyapunov-Razumikhin functions for time delay systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[15]  Frédéric Mazenc,et al.  Asymptotic tracking of a reference state for systems with a feedforward structure , 2000, Autom..

[16]  Henk Nijmeijer,et al.  Tracking Control of Mobile Robots: A Case Study in Backstepping , 1997, Autom..