Stability Of The Networked Control Systems With Time Delay

With the fast development of network technologies, network is applied to the controlfeld by researchers. The data received by the sensor is transmitted to the actuator throughthe network, The advantages a networked architecture has over the traditional point-to-point design are low cost of installation, fexibility, high resource utilization, simpleinstallation and ease of maintenance. This prompted the transformation from a traditionalarchitecture to a distributed architecture. Consequently there is a growing theoreticalinterest in the feld of networked control systems. i.e., the feedback control systems whosesensors, actuators and controllers are connected via communication networks. There aremany application (for example in aircraft automobiles and building automation) whereseveral sensors, actuators and control units share a common communication medium.In the meantime, the introduction of network makes the analysis and design of systemcomplexity. Conventional control theories with many ideal assumption must be reevalu-ated before they can be applied to networked control systems. Due to the sampling datatransmission through the network, the time delay is always inevitable. The time delay,either constant or time-varying, often causes deterioration of system performance andsystem instability. In the controller design, the stability of the system is the frst problemof consideration. Therefore, the networked control systems have attracted much researchinterest. This thesis studies the stability of several classes of networked control systemswith time delays.(1)We study the stability of the controlled continuous system with the time delayless than one sampling period and taking arbitrary values in a fnite interval. Consideringthe time-invariant state feedback controller, the network control system is modeled as aswitched system model. Sufcient conditions are obtained for exponential stability of theclosed-loop networked control system under a maximum packet-dropout rate. The designmethods of the state-feedback controller are got. Further we consider the anti-interferenceability of the controller, design the non-fragile state-feedback controller. The closed-loopnetworked control system is modeled as a discrete-time switched system. Through therobust control method and the matrix method. The criteria of non-fragile stability of thesystem are presented.(2)We study the H-infnity exponential stability problem for a class of networkedcontrol systems with time delay and packet dropout. Introduce the bufer, then the timedelay less than one sampling period takes values in a fnite set. Considering the time delayand packet dropout, the state feedback closed-loop networked control system is modeledas a discrete-time switched system. Each subsystem of the system corresponds to anevent. According to the two cases that the event rate is fxed and the switching signalmeet the Markov chain, sufcient conditions are obtained, respectively, under which the system is exponential stability with a desired H-infnity disturbance attenuation level. Bysolving a set of linear matrix inequalities, the designed H-infnity controller is obtained,respectively.(3) We study the stability of the networked control system with a Markovian jumplinear plant. Considering the random delays from the sensor to the controller and fromthe controller to the actuator, the closed-loop networked control system is modeled asa jump linear system with jumping parameters. The necessary and sufcient conditionsfor the stochastic stability of the system are respectively established under the functionof the state feedback controller and under the function of output feedback controller,respectively. The mode-dependent controllers are designed through the iterative linearmatrix inequality approach.(4)We study the stability of a class of uncertain networked control systems withquantization and time delay. Considering the time delay and the time-varying quantizerwith Markovian jumping characteristics, the networked control system is modeled asa switched linear system with uncertain parameters. By robust control method andstochastic control method, sufcient conditions for the stability of the closed-loop networkcontrol system are obtained. Through solving the linear matrix inequalities. the controllaws that depend on the mode of the quantizer and the value of the time delay areobtained.(5)We study the stability of switched network control systems with time delay. Con-sidering the time-varying delay and the time-varying sampling，we get the approximatesystem through Taylor series approximation approach, and model the approximate sys-tem as systems with polytopic uncertainty. Based on approximate discrete-time models,the switching-mode-dependent controller that can stabilize the approximate system is de-signed. Sufcient conditions for the stability of the closed-loop networked control systemsare provided.