The problem of absolute stability: A dynamic programming approach

Michael Margaliot, Rabin Gitizadeh

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1247-1252
Number of pages6
JournalAutomatica
Volume40
Issue number7
DOIs
StatePublished - Jul 2004

Keywords

  • Differential inclusions
  • Hamilton-Jacobi-Bellman equation
  • Hybrid systems
  • Switched linear systems

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