State controllability computation technique for linear time-varying systems by using taylor series approximation

Aksoy S.

International Journal of Adaptive Control and Signal Processing, vol.23, no.10, pp.907-925, 2009 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 10
  • Publication Date: 2009
  • Doi Number: 10.1002/acs.1066
  • Journal Name: International Journal of Adaptive Control and Signal Processing
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.907-925
  • Keywords: Controllability grammian matrix, Linear time-varying systems, Lyapunov differential matrix equation, State controllability, Taylor polynomials
  • İstanbul Ticaret University Affiliated: No

Abstract

This article presents a technique to determine the controllability grammian matrix (CGM) for linear time-varying systems by using truncated Taylor polynomial vector and the operational matrix of integration. An important property of this algorithm is that it starts by integrating the Lyapunov differential matrix equation in terms of the CGM. However, the algorithm does not use the mathematical integration processes actually, but uses the truncated Taylor polynomial vector and the operational matrix of integration. Thus, the problem is reduced to solving a linear set of algebraic equations with constant coefficients consisting of the Taylor polynomial constant coefficients of each of the CGM elements. Numerical results and error curves are given to illustrate the improvements achieved by the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.