The problem of absolute stability: a dynamic programming approach

Authors:
Michael Margaliot;Rabin Gitizadeh
Affiliations:
School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel;Department of Control and Simulation, IMI-ASD, Ramat Hasharon, Israel
Venue:
Automatica (Journal of IFAC)
Year:
2004

Citing 5
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Abstract

We consider the problem of absolute stability of a feedback system composed of a linear plant and a single sector-bounded nonlinearity. Pyatnitskiy and Rapoport used a variational approach and the Maximum Principle to derive an implicit characterization of the ''most destabilizing'' nonlinearity. In this paper, we address the same problem using a dynamic programming approach. We show that the corresponding value function is composed of simple building blocks which are the generalized first integrals of appropriate linear systems. We demonstrate how the results can be used to design stabilizing switched controllers.