Finite-Time Boundedness Control for Nonlinear Networked Systems with Randomly Occurring Multi-Distributed Delays and Missing Measurements

Abstract

This paper investigates the stochastic finite-time ∞ boundedness problem for nonlinear discrete time networked systems with randomly occurring multi-distributed delays and missing measurements. The randomly occurring multi-distributed delays and missing measurements are described as Bernoulli distributed white noise sequence. The goal of this paper is to design a full-order output-feedback controller to guarantee that the corresponding closed-loop system is stochastic finite-time ∞ bounded and with desired ∞ performance. By constructing a new Lyapunov-Krasovskii functional, sufficient conditions for the existence of outputfeedback are established. The desired full-order output-feedback controller is designed in terms of the solution to linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the designed method.

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

“…Conventional dissipative theory discussed the asymptotic behavior of the system over an infinite-time interval, while the proposed dissipative methods of this paper provide an input-output energy-related characterization to the analysis in a specified finite-time interval. On the other hand, the dissipative control considered in this paper is more general than most of existing finite-time stabilization, finite-time ∞ control, and FTP control [25][26][27][28][29][30][31], which contains ∞ performance and passive performance as two special cases by choosing appropriate parameters W, S, and R in inequality (10). When setting W = − , S = 0, and R = ( + 2 ) , the performance prescribed in Definition 6 becomes stochastic finite-time ∞ performance [27][28][29][30]; if W = 0, S = , and R = 2 , then it corresponds to FTP performance [31].…”

“…Example . We consider the same example in [28]; the system parameters are as follows: In addition, we take the following activation function:…”

“…According to the methods in [28], we can get the optimal values = 5.9474 and 2 = 11.5133, respectively. While using methods of this paper, we can obtain the optimal values…”

“…Yang et al dealt with the FTS for singular system [26]. Subsequently, FTS was extended to finite-time boundedness (FTB), the finite-time ∞ control, finite-time passive (FTP) control, and so on [27][28][29][30][31]. And recently, Ma et al studied the finite-time dissipative (FTD) problem of singular discrete-time Markov jump systems [32].…”

“…(2) By applying stochastic analysis method and LMI tool, sufficient conditions for the stochastic finite-time boundedness and stochastic finite-time dissipativity of the discrete-time NNS with Markovian jumps and mixed delays are given. Our model and conditions are more general than those given in [27][28][29][30]. (3) A more general controller is designed, that is, the nonfragile state feedback controller, which can greatly reduce conservation of the system.…”