Sampled-data control for Markovian switching neural networks with output quantization and packet dropouts

Abstract

This paper explores sampled-data control for Markovian switching neural networks (MSNNs) with dynamic output quantization and packet dropouts. The primary goal is to construct a multi-mode, quantized sampled-data controller that ensures stochastic stability and $H_{\infty }$ disturbance-reduction performance of the closed-loop MSNN. A Bernoulli-distributed random variable with uncertain probability is introduced to characterize the incidence of packet dropouts. To describe potential mode inconsistencies that may occur between the MSNN and controller, an exponential hidden Markov model is employed. Furthermore, the quantizer’s dynamic scaling factor is intentionally built as a piecewise function to avoid the potential division-by-zero problem. A sufficient condition for stochastic stability and $H_{\infty }$ disturbance-reduction performance is proposed, utilizing a mode- and time-dependent Lyapunov-type functional and several stochastic analysis tools. Then, through decoupling nonlinearities, a numerically efficient approach for determining the desired controller gains and parameter range associated with the dynamic scaling factor is developed. In order to facilitate comparisons, the situation with no uncertainty in the probability of packet dropouts is studied, and both analysis and design approaches are offered. Finally, two simulation examples are provided to validate the effectiveness and applicability of the developed approaches.