A numerically reliable approach to robust pole assignment for descriptor systems

  • Authors:

  • A. Varga

  • Affiliations:

  • German Aerospace Center, DLR--Oberpfaffenhofen, Institute of Robotics and Mechatronics, D-82234 Wessling, Germany

  • Venue:
  • Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
  • Year:
  • 2003

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Abstract

We propose a general, numerically reliable computational approach to solve the pole and eigenstructure assignment problem for descriptor systems. In the multi-input case, the proposed approach addresses the intrinsic non-uniqueness of the pole assignment problem solution by simultaneously minimizing the sensitivity of the feedback gain and of closed-loop eigenvalues. For this purpose, a minimum norm robust pole assignment problem is formulated and solved as an unconstrained minimization problem for a suitably chosen cost function. By using a generalized Sylvester equation-based parameterization, an explicit expression of the gradient of the cost function is derived to allow the efficient solution of the minimization problem by using powerful gradient search-based minimization techniques.