Generalised state estimation of Markov jump neural networks based on the Bessel–Legendre inequality

• Published in: IET control theory & applications Vol. 13; no. 9; pp. 1284 - 1290
• Main Authors: Shen, Hao, Jiao, Shiyu, Xia, Jianwei, Park, Ju H, Huang, Xia
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 11.06.2019
• Subjects: asymptotic stability; Bessel–Legendre inequality; delay systems; delays; generalised state estimation; Lyapunov methods; Markov jump neural networks; Markov jump static neural networks; Markov processes; neurocontrollers; observer; Special Issue: Recent Advances in Control and Verification for Hybrid Systems; stability; stability analysis; state estimation; stochastic systems; time delays; delay systems; stability analysis; Bessel–Legendre inequality; time delays; asymptotic stability; observer; Markov jump static neural networks; Markov jump neural networks; neurocontrollers; delays; Markov processes; stochastic systems; generalised state estimation; state estimation; stability; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5618

In the study, the authors are interested in investigating the stability analysis and state estimation of Markov jump static neural networks subject to time delays by the feat of Bessel–Legendre inequality. A canonical Bessel–Legendre inequality, which converts the limited interval $[-h, 0]$[−h,0] required in traditional Bessel–Legendre inequality to a general interval $[a, b]$[a,b] is employed. Accordingly, compared with the existing results, the restriction is naturally relaxed and the less conservative criterion is presented. The stability analysis is complicated after constructing an enhanced Lyapunov–Krasovskii functional suitable for the canonical Bessel–Legendre inequality. Furthermore, taking account of the information of system mode, the mode-dependent scheme is applied to the design of a state estimator. Corresponding results to the stability of the estimation error system and the acquisition of the desired observer are presented. In the end, an example, which proves the validity of the method is given.