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

Abstract

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.

Keywords

• complex-valued neural networks
• piecewise-homogeneous markovian switching
• stabilization
• incomplete transition rates