Analysis and control of a class of uncertain linear periodic discrete-time systems |
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Authors: | Kai Sun Guang-ming Xie |
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Institution: | LTCS and Center for Systems and Control, College of Engineering, Peking University,Beijing 100871, P. R. China;School of Electrical and Electronics Engineering,East China Jiaotong University,Nanchang 330013, P. R. China |
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Abstract: | Feedback control problems for linear periodic systems (LPSs) with intervaltype parameter uncertainties are studied in the
discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear
matrices inequality (LMI) for the asymptotical stability and state feedback stabilization, respectively, are given. Problems
of -gain analysis and control synthesis are studied. For the -gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and
has an -gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the
closed-loop system is asymptotically stable and has an -gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.
Project supported by the National Natural Science Foundation of China (Nos. 60404001 and 60774089) |
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Keywords: | linear periodic system parameter uncertainty robust stability linear ma-trix inequality (LMI) state feedback stabilization |
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