H∞ control for a networked Markovian jump system subject to data packet loss based on the observer

Abstract

This study researches the H ∞ control issue for a networked Markovian jump system with data packet loss occurring not only in the channel from sensor to controller but also in the channel from controller to actuator via an observer. The mathematical model for the closed-loop networked Markovian jump system with data packet loss is established. The necessary and sufficient conditions for the closed-loop system to be stochastically stable are derived. The design approach of the controller and the minimal performance index of the external disturbance suppression are also given in the case that the transition possibilities of the system modes and the data packet loss are both partially unavailable. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method. K E Y W O R D Sdata packet loss, Markovian jump system, networked control system, observer | INTRODUCTIONAs the networked control system (NCS) has the advantages of easy installation and maintenance, as well as convenient expansion, the application range of the NCS has become more and more extensive, including the fields of industrial systems, aerospace, robot manufacturing, remote sensing technology and so on [1][2][3][4]. Coupled with the increasing development of information technology, the NCS will be used in more fields in the future [5][6][7][8]. However, data packet loss and time-delay induced by the network would make the system's performance degrade and may even lead to instability, and these are two basic issues of the NCS [9][10][11][12][13].The research of data packet loss is a significant direction of NCS research, which has attracted considerable attention. For the current research study, there are mainly two approaches to deal with the problem of data packet loss. The first approach is to use a Bernoulli probability distribution sequence to describe the data packet loss as a random variable, which takes a value from f0; 1g [14][15][16][17]. The stability of the NCS whose communication channel was influenced by data packet loss was discussed [14], and a Bernoulli variable was used to model the data packet loss. Sliding mode control based on the observer for the NCS with quantisation was taken into consideration [15], in which data packet loss occurred when the measurement output was transmitted, and a compensating scheme was put forward to cope with influences of modelled data packet loss, which was treated as a Bernoulli process. A novel H ∞ approach for the NCS with multiple data packet losses was studied [16], and a control system containing two Bernoulli variables was applied to model the NCS, which contained not only measurement data packet loss but also control data packet loss. The problem of linear quadratic Gaussian control for the NCS with data packet loss was discussed [17], where dataThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.