Delay-dependent H _∞ stabilisation criterion for continuous-time networked control systems with random delays

Abstract

This article mainly addresses the H 1 stabilisation problem for a class of networked control systems (NCSs) with random input delays in the continuous-time domain. A Markov jump linear system (MJLS) model with two jump parameters is developed which takes both the sensor-to-controller and controller-to-actuator delays into account. Based on such a MJLS, a new Lyapunov-Krasovskii functional is proposed to establish a delay-dependent H 1 stabilisation criterion in terms of linear matrix inequalities (LMIs), and a mode-dependent state-feedback controller of NCSs can be determined. Two numerical examples are included to illustrate the derived result.

Networked control of discrete-time linear systems over lossy digital communication channels

“…Guo and Liu (2009) addressed observability and controllability of systems with limited data rate. Furthermore, control under communication constraints inevitably suffers signal transmission delay, date packet dropout and measurement quantisation which might be potential sources of instability and poor performance of control systems (Liu, Chai, Mu, and Rees 2008;Yang, Wang, and Yang 2008;Liu and Sun 2010;He, Wang, and Zhou 2012). The survey papers Baillieul and Antsaklis (2007) and Nair, Fagnani, Zampieri, and Evans (2007) gave a historical and technical account of the various formulations.…”

Modelling and Prediction of Random Delays in NCSs Using Double-Chain HMMs

“…As a result, hidden 2 with some other data. Markov models (HMMs) have been successfully used to model random delays of NCSs [28,29]. In the HMM-based delay model, the stochastic distribution of current delay is only governed by the current network state.…”

“…is kind of relationship between the network state and the random delay is referred to as an HMM. According to the delay characteristics, there are mainly three kinds of HMMs to model the random delays of NCSs: discrete-time HMM (DTHMM) [28,30], continuous-time HMM (CTHMM) [29,31], and semicontinuous HMM (SCHMM) [32]. Moreover, how to optimally initialize the parameters of HMM-based delay models has been discussed in [33].…”

“…Generally, the CA delay can arbitrarily take values from its acceptable interval, although only a certain discrete value is observed during each sampling period. is is the reason the continuous HMM [29,31] and semicontinuous HMM [32] have been used to model the CA delays. In these two models, the mixture Gaussian density functions are used to describe the distribution of the CA delays, which improves the modelling accuracy compared with the discrete HMM.…”

Modeling of Random Delays in Networked Control Systems

“…Based on the Lyapunov-Razumikhin method, a mode-dependent state feedback controller was designed to stabilize this class of systems by solving bilinear matrix inequalities. Based on the same delay modeling method as that in [77], a dynamic output feedback controller was designed to achieve both robust stability and prescribed disturbance attenuation performance for a class of uncertain NCSs with random delays in [78], and a new stochastic Lyapunov-Krasovskii function was proposed to develop a delay-dependent criterion for determining a mode-dependent state-feedback H ∞ controller for a class of continuous-time NCSs with random delays in [79]. In order to obtain less conservative results than those in [77], free weighting matrices were introduced in [79] by using the Newton-Leibniz formula to avoid estimating some crossterms in the Lyapunov-Krasovskii function.…”