Analysis of input-to-state stability for discrete time nonlinear systems via dynamic programming

Authors:
Shoudong Huang;Matthew R. James;Dragan NešIć;Peter M. Dower
Affiliations:
Centre of Excellence for Autonomous Systems, Faculty of Engineering, The University of Technology, Sydney, Australia;Department of Engineering, Australian National University, Canberra, ACT 0200, Australia;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:
2005

Citing 5
Cited 2

On characterizations of the input-to-state stability property

Systems & Control Letters
Extending H∞ control to nonlinear systems: control of nonlinear systems to achieve performance objectives

Extending H∞ control to nonlinear systems: control of nonlinear systems to achieve performance objectives
Lyapunov Characterizations of Input to Output Stability

SIAM Journal on Control and Optimization
Brief paper: A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

Automatica (Journal of IFAC)
Input-to-state stability for discrete-time nonlinear systems

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Fault coverage modeling in nonlinear dynamical systems

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Input-output robustness for discrete systems

Proceedings of the tenth ACM international conference on Embedded software

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Abstract

The input-to-state stability (ISS) property for systems with disturbances has received considerable attention over the past decade or so, with many applications and characterizations reported in the literature. The main purpose of this paper is to present analysis results for ISS that utilize dynamic programming techniques to characterize minimal ISS gains and transient bounds. These characterizations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimization problems in nonlinear dissipative systems theory (including L"2-gain analysis and nonlinear H"~ theory). As such, the results presented address an obvious gap in the literature.