Stability Analysis And Synthesis Of Networked Control Systems Based On Time-Varying Sampling Periods

The sampling period is often assumed to be constant in traditional control systems, but the assumption will not stand in networked control systems (NCSs). When the sampling period is time-varying, it is significant to study the modeling, analysis and controller design for Networked control systems.For Networked control systems, the shorter the sampling period, the better the system performance. Since the communication channels in Networked control systems are shared by multiple users, if the sampling period is short, the network load will increase inevitably. With the increase of information transmitted through communication channels, time delay and packet dropout is unavoidable, and network congestion will also occur, which may destroy the stability and performance of systems. If the sampling period is constant, it should be large enough to avoid network congestion, however, the network bandwidth can not be sufficiently used when the network is idle. To ensure the normal functioning and good system performance, the sampling period may be different when the network is busy or idle, which is called active varying sampling period methodology. On the other hand, the failure in control systems will also lead to time-varying sampling period, which will deteriorate system performance and stability, and it is called passive time-varying sampling period.This thesis study the modeling, analysis and controller design for Networked control systems with active time-varying sampling period and passive time-varying sampling period, and the main works are given as follows.First, the thesis studies on a class of NCSs with active time-varying sampling period. Suppose the sensor is both time driven and event driven, controller and actuator are event driven, the H∞controller design for Networked control systems with active time-varying sampling period, time delay and packet dropout is studied. Suppose the sampling period switch stochastically in a finite set, the Networked control systems with active time-varying sampling period are modeled as parameter-uncertain system, the sufficient conditions ensuring the asymptotic stability of systems are presented, and the problem of H∞controller design is converted into a LMI problem with multiple object optimization. The active time-varying sampling period method can ensure the sufficient use of network bandwidth, and the designed controller is also applicable for Networked control systems with constant sampling period.Second, the thesis studies on NCSs with passive time-varying sampling period driven by Markov chain, it consistes of three parts.Without considering the influence of time delay, passive time-varying sampling periods of continuous time linear time-invariant systems are modeled as Markov chain that switch in finite values, and the mathematics model for sampling control systems is presented; then the stochastic stability conditions for closed-loop systems are proposed, and the controller design is converted into a set of matrix inequalities, although the matrix inequalities are not linear, they can be transferred into linear matrix inequalities by using the cone complementarity approach, and the corresponding algorithm is given behind the theorem; then with the consideration of external disturbances, the sufficient conditions ensuring the H∞performance of systems are presented, and the controller design is transferred into an LMI problem.By considering the passive time-varying sampling period of continuous time linear time-invariant systems as distribution known and stochastic switching Markov chain, and considering the network-induced time delay which is independent on passive time-varying sampling period as distribution known, stochastic switching in finite values, the mathematics model is presented for sampling control system; then the sufficient and necessary conditions ensuring the stochastic stability of closed-loop system are proposed, and the problem of controller design is converted into the solution of matrix inequalities, which can also be solved by cone complementarity approach.The above two models are extended to more general Markov chain stochastic jumping system, and the sufficient and necessary conditions ensuring the stochastic stability of closed-loop system are presented. When there does not exist common controller, the designed model-dependent controller can ensure the stochastic stability of closed-loop system, the merits of the proposed methods are shown by numerical examples.Third, the thesis studies on a class of NCSs with passive time-varying sampling period and certain model. Considering continuous time linear time-invariant systems with network-induced time delay, packet dropout and passive time-varying sampling period, and the actuator may receive two or more than two control inputs during a sampling period, the model for sampling control system is presented. By using Jensen inequality and free weight matrix method, the sufficient conditions ensuring the asymptotic stability and H∞norm bounds are presented. The problem of H∞controller design is converted into a multiple object optimization problem with the constraint of a set of LMIs, which can be solved effectively. The proposed controller design is also applicable when the actuator receives zero or one control input during a sampling period. The given model is more general than the existing ones, and the designed controller can ensure better H∞performance and admissible maximum number of consecutive packet dropout than the existing results.