Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature

Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter

Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum (a∨b) and infimum (a∧b) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max-T fuzzy relation equations system

Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example