Decompositional Construction of Lyapunov Functions for Hybrid Systems
Decompositional Construction of Lyapunov Functions for Hybrid Systems
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DOI：
10.1007/978-3-642-00602-9_20
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发表时间：
2009-04
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影响因子：
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通讯作者：
Jens Oehlerking;Oliver E. Theel
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文献类型：
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作者：
Jens Oehlerking;Oliver E. Theel
本文提出了一种计算复杂离散状态空间混杂系统Lyapunov函数的自动机分解方法。我们使用基于图的推理将混合自动机分解成子图，然后针对子图求解半定优化问题以获得局部Lyapunov函数。这些局部计算保证了局部Lyapunov函数族形成全局Lyapunov函数，从而证明了系统的渐近稳定性。与标准LMI方法相比，LMI方法的主要优点是1)由于优化问题较小而提高了数值稳定性，2)可以增量地构造稳定的混合自动机，3)在找不到Lyapunov函数的情况下，更容易诊断自动机的不稳定部分。
In this paper, we present an automatable decompositional method for the computation of Lyapunov functions for hybrid systems with complex discrete state spaces. We use graph-based reasoning to decompose hybrid automata into subgraphs, for which we then solve semidefinite optimization problems to obtain local Lyapunov functions. These local computations are made in a way that ensures that the family of local Lyapunov functions forms a global Lyapunov function, proving asymptotic stability of the system. The main advantages over standard LMI methods are 1) improved numerical stability due to smaller optimization problems, 2) the possibility of incremental construction of stable hybrid automata and 3) easier diagnosis of unstable parts of the automaton in case no Lyapunov function can be found.