A Method for Estimating the Stability Region of Singular Perturbation Systems with Saturation Nonlinearities
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摘要: 针对奇异摄动饱和系统, 提出了一种估计其稳定域的降阶方法. 结合饱和函数的特殊性质, 证明了此类系统的稳定域可分解为伴随系统的不变集与一个足够大球体的笛卡尔积. 将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题, 利用线性矩阵不等式(Linear matrix inequality, LMI)优化方法估计伴随系统的稳定域以减少保守性. 本方法不仅可以克服奇异摄动饱和系统的奇异性, 还可以一定程度克服系统的``维数灾''等问题.Abstract: A reduced-order method was proposed for estimating the stability region of singular perturbation dynamical systems with saturation nonlinearities. Based on the properties of the saturation function, it was proved that the stability region of such dynamical systems can be decomposed into Cartesian product of an invariant set of their adjoint systems and a sufficiently large ball. The stability region estimation of the singularly perturbed systems can be replaced by that of the adjoint systems, and an optimization method based on linear matrix inequality was provided to reduce the conservativeness in the estimation. The proposed method can eliminate the singularity and overcome the dimension disaster to some extent.
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