Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays

• Published in: IEEE transaction on neural networks and learning systems 2020-12, Vol.31 (12), p.5456-5467
• Main Authors: Lin, Wen-Juan, He, Yong, Zhang, Chuan-Ke, Wu, Min
• Format: Article
• Language: English
• Subjects: Discrete-time neural networks (NNs); Discrete-time systems; finite-time <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ state estimation; H infinity; Linear matrix inequalities; Lyapunov methods; Mathematical models; Neural networks; semi-Markovian jump parameters; State estimation; Stochasticity; time-varying delay
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2020.2968074

In this article, the finite-time H ∞ state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H ∞ performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.