Brief paper: Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

  • Authors:

  • Zhan Shu;James Lam;Junlin Xiong

  • Affiliations:

  • Hamilton Institute, National University of Ireland, Maynooth, Maynooth, Co. Kildare, Ireland and Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra ACT 2600, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2010

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Abstract

This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical examples.