Observability gramian for nonlinear systems
Observability gramian for nonlinear systems
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非线性系统的可观测性格拉米亚
DOI：
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发表时间：
2007
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通讯作者：
U. Vaidya
中科院分区：
文献类型：
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作者：
U. Vaidya
本文提出了一种构造非线性系统能观性文法的新方法。对于线性系统，可观测性文法可归结为矩阵Lyapunov方程的解，对于非线性系统，可观测性文法信息可从Lyapunov测度方程的解中得到。Lyapunov测度方程在(U·Vaidya，2007)中被引入，给出了非线性系统中不变集几乎处处稳定的充要条件。线性系统的Gramian结果形成了所提出的利用传递算子的能观测性文法方法的特例。对于有输出测量的系统，我们使用面向集合的数值方法来对语法进行有限维近似。
In this paper, we propose a novel approach for the construction of observability gramian for nonlinear systems. For linear systems observability gramian is obtained as a solution of matrix Lyapunov equation, for nonlinear systems we show that the observability gramian information can be obtained from the solution of Lyapunov measure equation. Lyapunov measure equation is introduced in (U. Vaidya, 2007) to provide necessary and sufficient condition for almost every where stability of an invariant set in nonlinear systems. Gramian result for the linear systems forms a special case of the proposed observability gramian approach using transfer operator. For system with output measurement we use set oriented numerical methods are used for the finite dimensional approximation of the gramian.