Robust stability and stabilisation of discrete-time descriptor systems with uncertainties in the difference matrix

Author(s): W.-J. Mao
DOI: 10.1049/iet-cta.2011.0377

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Author(s): W.-J. Mao ¹
- Affiliations: 1: Institute of Cyber-Systems and Control, State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, People's Republic of China
Source: Volume 6, Issue 17, 15 November 2012, p. 2676 – 2685
DOI: 10.1049/iet-cta.2011.0377 , Print ISSN 1751-8644, Online ISSN 1751-8652

This study considers the problems of robust stability and stabilisation for linear discrete-time descriptor systems with norm-bounded uncertainties in all the system matrices including that in the difference matrix E. Under the assumption that the difference matrix E is rank-invariant for all admissible uncertainties, the robustness analysis problem under consideration falls into two cases: right-singular case and left-singular case. A necessary and sufficient stability condition and a sufficient stability condition are proposed for the first and second case, respectively. By using a state augmentation technique, sufficient stabilisation conditions are obtained for both cases. Furthermore, a necessary and sufficient stabilisation condition is established in the case of a non-singular matrix E. Finally, illustrative examples show that the proposed conditions are effective to design the stabilising controller for uncertain discrete-time descriptor systems with both the singular and non-singular matrixE.

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Robust stability and stabilisation of discrete-time descriptor systems with uncertainties in the difference matrix

Robust stability and stabilisation of discrete-time descriptor systems with uncertainties in the difference matrix

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