The Stability Condition Of The Network Control System Analysis And Controller Design

When the network control system (NCS) applies in practice, due to the limited bandwidth, such problems as network congestion, derivational time delay and stochastic dropout is inevitable. This paper based on the different method dealing with the dropout problem in terms of modeling, stability analysis and controller designing for NCS.Firstly, A four-way-drive open-loop mathematical model is established within one sampling period uncertain time delay, stochastic dropout and external disturbances.Secondly, a class of NCS with uncertain time delay and stochastic dropout is modeled as an asynchronous dynamical system with parameter uncertainties. Based on the Lyapunov stability theory, a sufficient condition is obtained for exponentially stable of NCS with both uncertain time delay and stochastic dropout, then a controller is designed. Simulation results demonstrate that the system has better robustness with the designed controller.Thirdly, by introducing the dropout compensator, the compensation control can be reduced to two subsystems when the network communication is under normal transmission and data dropout compensation, then this class of problem can be modeled as a class of stochastic switching discrete system with parameter uncertainties. Based on the Lyapunov stability theory and linear matrix equality (LMI) technology, then a sufficient condition for the stability of closed-loop system is obtained. In addition, an algorithm for robust guaranteed-cost controller is proposed. MATLAB simulations show the effectiveness of proposed controller.Finally, through the analysis of stochastic dropout, the NCS with stochastic dropout uncertain time-delay and external distribution can be modeled as a comprehensive system with stochastic sequence parameter and uncertainties. By using of stability definition of stochastic sequence parameter system, a sufficient condition is obtained to ensure the stability of system. According to the sufficient condition, the method of designing H∞optimal controller is obtained. By solving LMI, an optimal H∞controller is designed. Simulation results illustrate that the robust optimal H∞controller makes the system quicker to reach the equilibrium point.