Non-uniform in time robust global asymptotic output stability for discrete-time systems

In this paper the notions of non-uniform in time robust global asymptotic output stability (RGAOS) and input-to-output stability (IOS) for discrete-time systems are studied. Characterizations as well as links between these notions are provided. Particularly, it is shown that a discrete-time system with continuous dynamics satisfies the non-uniform in time IOS property if and only if the corresponding unforced system is non-uniformly in time RGAOS. Necessary and sufficient conditions for the solvability of the robust output feedback stabilization (ROFS) problem are also given. Copyright © 2005 John Wiley & Sons, Ltd.

[1]  Andrew R. Teel,et al.  Smooth Lyapunov functions and robustness of stability for difference inclusions , 2004, Syst. Control. Lett..

[2]  Andrew R. Teel,et al.  Results on converse Lyapunov theorems for difference inclusions , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[4]  Pierdomenico Pepe,et al.  The Liapunov's second method for continuous time difference equations , 2003 .

[5]  Iasson Karafyllis,et al.  The Non-uniform in Time Small-Gain Theorem for a Wide Class of Control Systems with Outputs , 2004, Eur. J. Control.

[6]  Eduardo Sontag,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999, at - Automatisierungstechnik.

[7]  Riccardo Scattolini,et al.  On the stabilization of nonlinear discrete-time systems with output feedback , 2004 .

[8]  Zhong-Ping Jiang,et al.  A converse Lyapunov theorem for discrete-time systems with disturbances , 2002, Syst. Control. Lett..

[9]  Zhong-Ping Jiang,et al.  Nonlinear small-gain theorems for discrete-time feedback systems and applications , 2004, Autom..

[10]  Thomas Parisini,et al.  A neural state estimator with bounded errors for nonlinear systems , 1999, IEEE Trans. Autom. Control..

[11]  Eduardo Sontag.  Comments on integral variants of ISS , 1998 .

[12]  J. Gauthier,et al.  Deterministic Observation Theory and Applications , 2001 .

[13]  Iasson Karafyllis,et al.  Robust output feedback stabilization and nonlinear observer design , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  J. Tsinias,et al.  Stabilization of nonlinear discrete-time systems using state detection , 1993, IEEE Trans. Autom. Control..

[15]  B. Kouvaritakis,et al.  Observers in nonlinear model-based predictive control , 2000 .

[16]  C. Byrnes,et al.  Design of discrete-time nonlinear control systems via smooth feedback , 1994, IEEE Trans. Autom. Control..

[17]  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..

[18]  Eduardo D. Sontag,et al.  Lyapunov Characterizations of Input to Output Stability , 2000, SIAM J. Control. Optim..

[19]  Eduardo Sontag,et al.  Notions of input to output stability , 1999, Systems & Control Letters.

[20]  F. Allgöwer,et al.  Output feedback stabilization of constrained systems with nonlinear predictive control , 2003 .

[21]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[22]  Brian Ingalls,et al.  On Input-to-Output Stability for Systems not Uniformly Bounded , 2001 .

[23]  Yuan Wang,et al.  A local nonlinear small-gain theorem for discrete-time feedback systems , 2000 .

[24]  Iasson Karafyllis,et al.  Non-uniform robust global asymptotic stability for discrete-time systems and applications to numerical analysis , 2006, IMA J. Math. Control. Inf..

[25]  A. Teel,et al.  Tools for Semiglobal Stabilization by Partial State and Output Feedback , 1995 .