Stability analysis of grey neural networks with application in psychological counseling evaluation system

Purpose Recent studies have utilized switched neural networks to model the psychological counseling evaluation system (PCES). Analyzing the stability of these network models effectively and efficiently is critical for their practical application. This paper aims to investigate the robust exponential stability of the switched complex-valued grey neural networks (SCGNNs) under both arbitrary and restricted switching. Design/methodology/approach Firstly, a mapping related to SCGNNs is constructed and shown to be a homeomorphism under specific conditions, which establishes the uniqueness of the equilibrium point in SCGNNs. Secondly, an appropriate Lyapunov function is formulated, and inequality techniques, combined with the impulsive average dwell time method, are utilized to demonstrate that the Lyapunov function decreases along the solution trajectories of SCGNNs. This analysis proves the stability of the system under both arbitrary and restricted switching. Finally, a simulation example of evaluating the effectiveness of psychological counseling is provided to verify the correctness and validity of the proposed findings. Findings When the system parameters and external inputs are represented as interval grey numbers, conditions are separately derived for the existence and uniqueness of the system’s equilibrium point and for its robust exponential stability under both arbitrary and restricted switching. Originality/value (1) In Zhang et al. (2022), the stability of SCGNNs under restricted switching was studied, whereas this paper focuses on the stability of SCGNNs under arbitrary switching. This is particularly relevant for systems, such as PCES, where the switching signal cannot be predetermined. Additionally, this paper examines the influence of impulsive disturbances on system stability. (2) New analytical methods and a novel Lyapunov function are utilized, leading to conditions for the existence and stability of the equilibrium points with reduced conservatism.