Local Asymptotic Stability via Averaging for Time-Varying Systems With Unbounded Dynamics With Respect to Time

The purpose of this note is to provide sufficient conditions for asymptotic stability for time-varying systems, whose dynamics are unbounded with respect to time. An averaging approach is established that constitutes a generalization of the well known methodology adopted in the literature for systems whose dynamics are bounded with respect to time.

[1]  Iasson Karafyllis,et al.  Non-Uniform in Time State Estimation of Dynamical Systems , 2004 .

[2]  J. Tsinias,et al.  Time-varying observers for a class of nonlinear systems , 2008, Syst. Control. Lett..

[3]  H. Kushner,et al.  On the stability of randomly sampled systems , 1969 .

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

[5]  A. Teel,et al.  Semi-global practical asymptotic stability and averaging , 1999 .

[6]  Michael Malisoff,et al.  On strict Lyapunov functions for rapidly time-varying nonlinear systems , 2006 .

[7]  Dragan Nesic,et al.  A Trajectory-Based Approach for the Stability Robustness of Nonlinear Systems with Inputs , 2002, Math. Control. Signals Syst..

[8]  Dragan Nesic,et al.  Averaging with disturbances and closeness of solutions , 2000 .

[9]  Dragan Nesic,et al.  Input-to-State Stability for Nonlinear Time-Varying Systems via Averaging , 2001, Math. Control. Signals Syst..

[10]  Dirk Aeyels,et al.  On exponential stability of nonlinear time-varying differential equations , 1999, Autom..

[11]  Peter Seiler,et al.  Estimation with lossy measurements: jump estimators for jump systems , 2003, IEEE Trans. Autom. Control..

[12]  I. Karafyllis,et al.  Non-uniform in time stabilization for linear systems and tracking control for non-holonomic systems in chained form , 2003 .

[13]  J. Tsinias.  A converse Lyapunov theorem for, non-uniform in time, global exponential robust stability , 2001, Syst. Control. Lett..

[14]  V. I. Vorotnikov.  Partial stability and control , 1998 .

[15]  Yuandan Lin,et al.  A Smooth Converse Lyapunov Theorem for Robust Stability , 1996 .

[16]  Dirk Aeyels,et al.  Averaging Results and the Study of Uniform Asymptotic Stability of Homogeneous Differential Equations That Are Not Fast Time-Varying , 1999 .

[17]  Iasson Karafyllis,et al.  Control Lyapunov functions and stabilization by means of continuous time-varying feedback , 2007 .

[18]  Panos J. Antsaklis,et al.  Stability of model-based networked control systems with time-varying transmission times , 2004, IEEE Transactions on Automatic Control.

[19]  Subhrakanti Dey,et al.  Stability of Kalman filtering with Markovian packet losses , 2007, Autom..

[20]  Frank Kozin,et al.  A survey of stability of stochastic systems , 1969, Autom..

[21]  Iasson Karafyllis,et al.  A Converse Lyapunov Theorem for Nonuniform in Time Global Asymptotic Stability and Its Application to Feedback Stabilization , 2003, SIAM J. Control. Optim..

[22]  Dirk Aeyels,et al.  Exponential Stability of Nonlinear Time-Varying Differential Equations and Partial Averaging , 2002, Math. Control. Signals Syst..

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