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首页> 外文期刊>Automatic Control, IEEE Transactions on >Hybrid Stabilization of Linear Systems With Reverse Polytopic Input Constraints
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Hybrid Stabilization of Linear Systems With Reverse Polytopic Input Constraints

机译：具有反向多边形输入约束的线性系统的混合镇定

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摘要

This paper addresses the problem of globally uniformly exponentially stabilizing a linear system to the origin by output feedback while avoiding a prescribed set of input values. We consider that the set of input values to avoid is given by the union of a finite number of closed polytopes that do not contain the origin and we refer to this restriction as a reverse polytopic input constraint. We show that the synthesis of the hybrid controller can be performed by solving a set of linear matrix inequalities for the full-state feedback case, and by solving a set of bilinear matrix inequalities for the output feedback case. The resulting closed-loop hybrid system is shown to satisfy key conditions for well-posedness and robustness to small measurement noise. Furthermore, we apply the proposed hybrid controller to the stabilization of a single-input linear system subject to reverse polytopic constraints on the norm of the input. The behavior of the corresponding closed-loop hybrid system is validated by simulations.
机译：本文解决了通过避免输入信号的规定集合同时通过输出反馈使线性系统全局均匀地稳定到原点的问题。我们认为应避免的输入值集由不包含原点的有限数量的封闭多面体的并集给出，我们将此限制称为反向多面体输入约束。我们表明，混合控制器的综合可以通过为全状态反馈情况求解一组线性矩阵不等式，以及为输出反馈情况求解一组双线性矩阵不等式来执行。结果表明，所得的闭环混合系统满足关键条件，具有良好的适定性和对小测量噪声的鲁棒性。此外，我们将提出的混合控制器应用于单输入线性系统的稳定性，该线性系统受到对输入范数的反向多边形约束。通过仿真验证了相应闭环混合系统的行为。

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