Positive real control for uncertain two-dimensional systems
(2002) IEEE Transactions on Circuits and Systems Part 1: Fundamental Theory and Applications — Vol. 49, n° 11, p. 1659-1666 (2002)
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- Abstract
- This brief, deals with the problem of positive real control for uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini local state-space model. The parameter uncertainty is time-invariant and norm-bounded. The problem we address is the design of a state feedback controller that robustly stabilizes the uncertain system and achieves the extended strictly positive realness of the resulting closed-loop system for all admissible uncertainties. A version of positive realness for 2-D discrete systems is established. Based on this, a condition for the solvability of the positive real control problem is derived in terms of a linear matrix inequality. Furthermore, the solution of a desired. state feedback controller is also given. Finally, we provide a numerical example to demonstrate the applicability of the proposed approach.
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Xu, S., Lam, J., Lin, Z., & Galkowski, K. (2002). Positive real control for uncertain two-dimensional systems. IEEE Transactions on Circuits and Systems Part 1: Fundamental Theory and Applications, 49(11), 1659-1666. https://doi.org/10.1109/TCSI.2002.804531 (Original work published 2002)