Improved Results on Guaranteed Generalized $${\mathcal {H}}_{2}$$ H 2 Performance State Estimation for Delayed Static Neural Networks

Abstract

This paper is concerned with the guaranteed generalized $${\mathcal {H}}_{2}$$ performance state estimation for a class of static neural networks with a time-varying delay. A more general Arcak-type state estimator rather than the Luenberger-type state estimator is adopted to deal with this problem. Based on the Lyapunov stability theory, the inequality techniques and the delay-partitioning approach, some novel delay-dependent design criteria in terms of linear matrix inequalities (LMIs) are proposed ensuring that the resulting error system is globally asymptotically stable and a prescribed generalized $${\mathcal {H}}_{2}$$ performance is guaranteed. The estimator gain matrices can be derived by solving the LMIs. Compared with the existing results, the sufficient conditions presented in this paper are with less conservatism. Numerical examples are given to illustrate the effectiveness and superiority of the developed method over the existing approaches. A comparison between the Arcak-type state estimator and Luenberger-type state estimator is given simultaneously.