Robust Stabilization of Discrete-Time Uncertain Nonlinear Systems

A. V. Savkin and I. R. Petersen
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A. V. Savkin: University of Western Australia
I. R. Petersen: School of Electrical Engineering, Australian Defence Force Academy

Journal of Optimization Theory and Applications, 1998, vol. 96, issue 1, No 3, 87-107

Abstract: Abstract This paper applies a recent result on nonlinear H ∞-optimal control to give a necessary and sufficient condition for the existence of a state feedback controller which absolutely stabilizes a discrete-time uncertain nonlinear system with structured uncertainty. The class of uncertain systems being considered contain uncertainties which satisfy a certain sum constraint. This sum constraint is a nonlinear discrete-time version of the integral quadratic constraint uncertainty description. The main result is established by using a nonlinear S-procedure result, which enables the robust absolute stabilization problem to be converted into a equivalent nonlinear H∞-optimal control problem.

Keywords: H ∞-optimal control; nonlinear systems; uncertain systems; absolute stabilizability; structured uncertainty; nonlinear S-procedure; discrete-time systems (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022611116645

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