The problem of absolute stability: A dynamic programming approach

Michael Margaliot, Rabin Gitizadeh

Research output: Contribution to journalArticlepeer-review


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
Issue number7
StatePublished - Jul 2004


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


Dive into the research topics of 'The problem of absolute stability: A dynamic programming approach'. Together they form a unique fingerprint.

Cite this