Input-to-state stability for parameterized discrete-time time-varying nonlinear systems with applications

Input-to-state stability (ISS) of a parameterized family of discrete-time time-varying nonlinear systems is investigated. A converse Lyapunov theorem for such systems is developed. We consider parameterized families of discrete-time systems and concentrate on a semiglobal practical property that naturally arises when an approximate discrete-time model is used to design a controller for a sampled-data system. Application of our main result to time-varying periodic systems is presented. This is then used to design a semiglobal practical ISS (SP-ISS) control law for the model of a wheeled mobile robot.

[1]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[2]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[3]  Dragan Nesic,et al.  A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models , 2004, IEEE Transactions on Automatic Control.

[4]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[5]  Richard M. Murray,et al.  Nonholonomic control systems: from steering to stabilization with sinusoids , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[6]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[7]  Dragan Nesic,et al.  Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications , 2003, Autom..

[8]  Eduardo D. Sontag,et al.  FEEDBACK STABILIZATION OF NONLINEAR SYSTEMS , 1990 .

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

[10]  A. R. Teelb,et al.  Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems , 1999 .

[11]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[12]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[13]  A. R. Humphries,et al.  Dynamical Systems And Numerical Analysis , 1996 .

[14]  Yuandan Lin.  Input-to-State Stability with Respect to Noncompact Sets 1 , 1996 .

[15]  Dragan Nesic,et al.  Open- and Closed-Loop Dissipation Inequalities Under Sampling and Controller Emulation , 2002, Eur. J. Control.

[16]  O. Egeland,et al.  A Lyapunov approach to exponential stabilization of nonholonomic systems in power form , 1997, IEEE Trans. Autom. Control..

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

[18]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[19]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[20]  Eduardo Sontag,et al.  Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems , 1999 .

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

[22]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems using homogeneous feedback , 1997, IEEE Trans. Autom. Control..

[23]  Yuandan Lin,et al.  On input-to-state stability for time varying nonlinear systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[24]  Eduardo D. Sontag,et al.  The ISS philosophy as a unifying framework for stability-like behavior , 2001 .

[25]  Dragan Nesic,et al.  On uniform asymptotic stability of time-varying parameterized discrete-time cascades , 2004, IEEE Transactions on Automatic Control.

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