State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals
State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals
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DOI：
10.3390/math8091424
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发表时间：
2020-08
期刊：
影响因子：
2.4
通讯作者：
A. Alessandri;P. Bagnerini;R. Cianci
中科院分区：
文献类型：
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作者：
A. Alessandri;P. Bagnerini;R. Cianci
具有Lipschitz非线性系统的状态观测器被认为是什么关系到的估计误差的稳定性，通过分解的动态误差到两个系统的级联。首先，建立条件，以保证在无噪声设置的估计误差的渐近稳定性。第二，在系统和测量干扰的影响下，被视为未知的输入影响的动态误差，建议的观察员提供的估计误差是输入状态稳定的这些干扰。利用李雅普诺夫函数和泛函证明了这些结果。第三，仿真结果证实了我们所建立的理论成果和稳定性条件的有效性。
State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.