Finite‐Time Nonfragile Dissipative Control for Discrete‐Time Neural Networks with Markovian Jumps and Mixed Time‐Delays

Abstract

This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discrete-time neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays. First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. Then, the main results are extended to SFTD control. Furthermore, existence condition of nonfragile controller is derived based on solution of linear matrix inequalities (LMIs). Finally, two numerical examples are employed to show the effectiveness of the obtained methods.

Event-Triggered Extended Dissipativity Fuzzy Filter Design for Nonlinear Markovian Switching Systems against Deception Attacks

“…A Markovian jump system is a stochastic hybrid system that has finite modes of operation, where jumps between modes are controlled by a Markov process. Several recent research studies have focused on MJSs, resulting in significant publications about fault tolerance, target tracking, manufacturing, networked control, and multi-agent systems [1][2][3][4][5][6]. Despite many successes in this research, most practical systems are highly nonlinear, so linear MJSs impose marked limitations in real-world applications.…”

Output feedback finite‐time dissipative control for uncertain nonlinear fractional‐order systems

“…Remark 3. As far as we know, there are a lot of literatures on finite-time dissipative control of integer-order dynamical systems (IODS) [25][26][27][28][29][30][31][32][33][34]. These results derived in the form of LMI by using Lyapunov method.…”

“…By employing Lyapunov function technique together with Wirtinger-based integral inequalities, the authors in [27] addressed the problem of FD-based fault-tolerant control of Takagi-Sugeno fuzzy systems in a network environment. Likewise, Y. Ma and Chen and L. Hou et al have derived some novel results for non-fragile control [28,29]. Recently, by employing LMI-based optimization algorithm, sufficient conditions that ensure the finite-time boundedness with dissipativity of the large-scale systems were obtained [30].…”