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

Abstract The notions of non-uniform in time Robust Global Asymptotic Output Stability and robust forward completeness for time-varying systems are introduced. Necessary and sufficient conditions and Lyapunov-like characterizations are given for these notions.

[1]  Iasson Karafyllis,et al.  Robust output feedback stabilization and nonlinear observer design , 2005, Syst. Control. Lett..

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

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

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

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

[6]  A. Teel,et al.  A Smooth Lyapunov Function from a Class-kl Estimate Involving Two Positive Semideenite Functions , 1999 .

[7]  Aaron Strauss,et al.  On the global existence of solutions and Liapunov functions , 1967 .

[8]  Iasson Karafyllis Necessary and sufficient conditions for the existence of stabilizing feedback for control systems , 2003, IMA J. Math. Control. Inf..

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

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

[11]  Eduardo Sontag,et al.  Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations , 1999 .

[12]  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.

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

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

[15]  A. Teel,et al.  A smooth Lyapunov function from a class- ${\mathcal{KL}}$ estimate involving two positive semidefinite functions , 2000 .

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

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

[19]  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..

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

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

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

[23]  David Angeli,et al.  A characterization of integral input-to-state stability , 2000, IEEE Trans. Autom. Control..

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

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

[26]  Shouchuan Hu Differential equations with discontinuous right-hand sides☆ , 1991 .

[27]  Iasson Karafyllis,et al.  Nonuniform in time input-to-state stability and the small-gain theorem , 2004, IEEE Transactions on Automatic Control.

[28]  I. Karafyllis,et al.  Global stabilization and asymptotic tracking for a class of nonlinear systems by means of time‐varying feedback , 2003 .

[29]  Iasson Karafyllis,et al.  Non‐uniform stabilization of control systems , 2002 .

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

[31]  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).

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

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

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

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