On the computation of the gap metric for LTV systems

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• 作者：Seddik M. Djouadi ; Yanyan Li
• 关键词：Robust stabilization ; Robust control ; Time-varying ; Optimal control
• 刊名：Systems and Control Letters
• 出版年：2007
• 出版时间：November-December 2007
• 年：2007
• 卷：56
• 期：11-12
• 页码：753-758
• 全文大小：172 K

文摘

In this paper, we consider the robust stabilization problem for linear discrete time-varying (LTV) systems using the gap metric. In particular, we show that the time-varying (TV) directed gap reduces to an operator with a TV Hankel plus Toeplitz structure. Computation of the norm of such an operator can be carried out using an iterative scheme involving a TV Hankel operator defined on a space of Hilbert–Schmidt causal operators. The “infimization” in the TV directed gap formula is shown to be, in fact, a minimum by using duality theory. The latter holds as well in the time-invariant case.