Nonlinear Dyn DOI 10.1007/s11071-013-0783-1 ORIGINAL PAPER Sampled-data state estimation for delayed neural networks with Markovian jumping parameters Jiawen Hu · Nan Li · Xiaohui Liu · Gongxuan Zhang Received: 1 November 2012 / Accepted: 17 January 2013 © Springer Science+Business Media Dordrecht 2013 Abstract This paper is concerned with the sampled- data state estimation problem for a class of delayed neural networks with Markovian jumping parameters. Unlike the classical state estimation problem, in our state estimation scheme, the sampled measurements are adopted to estimate the concerned neuron states. The neural network under consideration is assumed to have multiple modes that switch from one to another according to a given Markovian chain. By utilizing the input delay approach, the sampling period is converted into a time-varying yet bounded delay. Then a suffi- cient condition is given under which the resulting error dynamics of the neural networks is exponentially sta- ble in the mean square. Based on that, a set of sampled- data estimators is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using the available software. Finally, a nu- merical example is used to show the effectiveness of the estimation approach proposed in this paper. J. Hu ( ) College of Electromechanical Engineering, Zhejiang Ocean University, Zhoushan 316004, China e-mail: jiawenhuzhy@gmail.com N. Li School of Information Science and Technology, Donghua University, Shanghai 200051, China X. Liu · G. Zhang School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China Keywords Markovian chain · Neural networks · State estimation · Sampled measurements · Time delay 1 Introduction The past few decades have witnessed constant re- search interest in various aspects of neural networks due mainly to the fact that neural networks have been extensively applied in many fields such as image pro- cessing, pattern recognition, associative memory and optimization problems. In these applications, the neu- ron states are usually required to be known so as to achieve certain performance objects. However, it is not the case sometimes in the practice, and only partial in- formation about the neuron states is available via the output of networks. Therefore, it is of vital importance to estimate the neuron states by using the available measurement outputs. This is customarily referred to as a state estimation problem of neural networks and, in the past decade, considerable research efforts have been made on this topic. For example, in [13], state es- timation problems have been studied for continuous- time neural networks while, in [4], similar problems have been considered for the discrete-time case. In [2, 16], the state estimation problems have been inves- tigated for various delayed neural networks where the considered time-delays include distributed delays, in- terval time-varying delays and mixed mode-dependent delays. In [17], a new type of neural networks, i.e.,