Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications

  • Authors:

  • Dina Shona Laila;Dragan NešIć

  • Affiliations:

  • Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, 3010, Victoria, Australia;Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, 3010, Victoria, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

We present results on changing supply rates for input-output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.