Robust stability and stabilization of discrete singular systems: an equivalent characterization

By Shengyuan Xu, James Lam. IEEE Transactions on Automatic Control, 2004

332 citations recorded by the source corpus.

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/87c8068c9e71bc3706d4a2128ea2a88ba9a18d15

How researchers see this paper

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In Computational Theory and Mathematics

1. H. Su
2. Jian Chu
3. Zhengguang Wu
4. Shuping Ma
5. Chenghui Zhang
6. Fanbiao Li
7. Peng Shi
8. Xian Zhang

In Control and Systems Engineering

1. H. Su
2. Jian Chu
3. Zhengguang Wu
4. Shuping Ma
5. Chenghui Zhang
6. Fanbiao Li
7. Peng Shi
8. Xian Zhang

Citations in the corpus

• Stability and stabilization of continuous descriptor systems: An LMI approach (2006, unknown): “Let us quote for instance controllability and observability, pole assignment, stability analysis [8, 10], and stabilization techniques as well as results including robustness aspects [9, 12, 17].”
• Stability and stabilization of discrete‐time singular Markov jump systems with time‐varying delay (2010, unknown): “Definition 1 (Xu and Lam [16]) System Exk+1= A(rk)xk (or the pair (E, A(rk))) is said to be 1.”
• Robust stabilization for uncertain discrete singular systems with state delay (2008, background): “Xu et al. [16], Xu and Lam [17], Chen and Chou [18, 19] discussed the robust stability problem for discrete singular systems with state delay and uncertainty and established several robust stability and D-stability conditions.”
• Robust stability and H∞ control for uncertain discrete Markovian jump singular systems with mode‐dependent time‐delay (2009, background): “For example, Ma and Cheng [18], Xu and Lam [19] gave some results on robust stability and robust stabilization for discrete singular systems.”