A Dual to Lyapanov's Second Method for Linear Systems with Multiple Delays and Implementation using SOS

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We present a dual form of Lyapunov-Krasovskii functional which allows the problem of controller synthesis for multi-delay systems to be formulated and solved in a convex manner. First, we give a generalized version of the dual stability condition formulated in terms of Lyapunov operators which are positive, self-adjoint and preserve the structure of the state-space. Second, we provide a class of such operators and express the stability conditions as positivity and negativity of quadratic Lyapunov-Krasovskii functional forms. Next, we adapt the SOS methodology to express positivity and negativity of these forms as LMIs, describing a new set of polynomial manipulation tools designed for this purpose. We apply the resulting LMIs to a battery of numerical examples and demonstrate that the stability conditions are not significantly conservative. Finally, we formulate a test for controller synthesis for systems with multiple delays, apply the test to a numerical example, and simulate the resulting closed-loop system.

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
DOIs
StateAccepted/In press - May 1 2018

Keywords

  • Asymptotic stability
  • Controller Synthesis
  • Delay Systems
  • Delays
  • LMIs
  • Lyapunov methods
  • Numerical stability
  • Optimization
  • Stability criteria

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'A Dual to Lyapanov's Second Method for Linear Systems with Multiple Delays and Implementation using SOS'. Together they form a unique fingerprint.

  • Cite this