Stabilization of piecewise-homogeneous Markovian switching CVNNs with mode-dependent delays and incomplete transition rates

• Main Authors: Qiang Li, Jinling Liang, Weiqiang Gong
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2020-01-01
• Series: Systems Science & Control Engineering
• Subjects: complex-valued neural networks; piecewise-homogeneous markovian switching; stabilization; incomplete transition rates
• Online Access: http://dx.doi.org/10.1080/21642583.2020.1737847

This paper is devoted to the problems of exponential stability and stabilization for piecewise-homogeneous Markovian switching complex-valued neural networks with incomplete transition rates (TRs). Both the time-varying delays and the coefficient matrices are switched among finite modes governed by a piecewise-homogeneous Markov process, where the TRs of the two-level Markov processes are assumed to be time-varying during different intervals. On the basis of an appropriately chosen Lyapunov–Krasovskii functional, some mode-dependent sufficient conditions are presented to guarantee the unforced network to be exponentially mean-square stable. Then, by proposing certain mode-dependent state feedback controller, stabilization criteria are derived through strict mathematical proofs. At the end of the paper, numerical examples are provided to illustrate the effectiveness of the theoretical results.