Abstract
The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.
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This work was partially supported by RGC Grant 7103/01P and the open project of the state key Laboratory of intelligent and Systems, Tsinghua University (No.0406).
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Zhou, S., Lam, J. & Xu, S. Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices. J. Control Theory Appl. 2, 75–81 (2004). https://doi.org/10.1007/s11768-004-0027-5
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DOI: https://doi.org/10.1007/s11768-004-0027-5