摘要：AbstractThe increasing utilization of recurrent neural networks (RNNs) in feedback control and the complexity of RNNs motivate us to provide a method for verifying the stability of RNN-controlled systems. To circumvent the nonlinearities in RNNs, we describe them using local integral quadratic constraints. A sufficient condition based on linear matrix inequalities is achieved for local asymptotic stability of feedback interconnections between a linear time-invariant plant and an RNN controller. This condition is employed as a constraint to construct semidefinite programming for finding a large ellipsoidal inner approximation to the region of attraction. A bisection algorithm is proposed to enlarge the inner approximation further. A necessary condition for local asymptotic stability is derived from linearization, which can be exploited to determine initial values for the bisection algorithm. Illustrative examples complete the presentation and show the improvement by our work.
关键词：Keywordsstability analysisrecurrent neural networksintegral quadratic constraintssemidefinite programmingregion of attraction
