Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

Abstract

Abstract-In this paper, the robust filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts. A sequence of random variables, all of which are mutually independent but obey Bernoulli distribution, are introduced to account for the randomly occurred communication delays. The packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. The discrete-time system under consideration is also subject to parameter uncertainties, state-dependent stochastic disturbances and sector-bounded nonlinearities. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed performance for the overall filtering error dynamics, in the presence of random delays, random dropouts, nonlinearities, and the parameter uncertainties. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper.Index Terms-Networked systems, nonlinear systems, packet dropout, robust filtering, stochastic systems, stochastic time-varying communication delays.

Recent Progress in Stability and Stabilization of Systems with Time-Delays

“…(vii) The class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts was addressed in [84] for filtering design and in [85] for reliable control. A promising research direction is to extend the role of delay patterns to alternative forms.…”

Estimation, filtering and fusion for networked systems with network-induced phenomena: New progress and prospects

“…Note that most of the relevant results have been concerned with the deterministic delays only, while the communication delays induced by network transmissions would be random and time-varying. As such, the random communication delays have received some initial research interests and the problems of estimation, filtering and fusion have been studied for networked systems with random communication delays [39], [90]- [93]. For example, the filtering problems have been studied in [39], [90], [92], [93] for networked systems with random communication delays modeled by Bernoulli random variables.…”

“…As such, the random communication delays have received some initial research interests and the problems of estimation, filtering and fusion have been studied for networked systems with random communication delays [39], [90]- [93]. For example, the filtering problems have been studied in [39], [90], [92], [93] for networked systems with random communication delays modeled by Bernoulli random variables. In [91], the optimal filtering problem has been investigated for networked systems with random communication delays modeled by Markov chain.…”

Particle filtering with applications in networked systems: a survey

“…A large number of papers have been published on filter design for systems with multiple network-induced phenomena. For example, the simultaneous presence of time delay and packet loss has been addressed in [89][90][91]; both quantization and packet dropout have been taken into consideration in [92]; a filtering scheme has been recently proposed in [93] which is robust against both channel fadings and gain variations. For more related results, the readers are referred to [94][95][96][97][98][99][100][101].…”