Stability And Control Of Interconnected Large-Scale Systems With Time Delays

Based on the theory of topology and the properties of M-matrix, by constructing vector Liapunov function and applying differential inequalities, the exponential stability of three classes of interconnected large-scale systems with time delays is analyzed. From the stability theory of large-scale systems, the longitudinal following control strategy of vehicles in a platoon in Intelligent Transportation Systems (ITS) is studied. In the first part, a sufficient condition is obtained for global exponential stability of a class of linear interconnected large-scale system with delays, the exponential convergence rate is estimated, and an example is given to demonstrate the feasibility of the criterion. In the second part., the global exponential stability of a class of nonlinear large-scalesystems with time delays-Fuzzy Cellular Neural Networks (FCNNs) withtime-varying delays is studied, without assuming the boundedness and differentiability of the activation functions, the sufficient conditions ensuring existence, uniqueness, and globally exponential stability of the equilibrium point of fuzzy cellular neural networks with variable delays are obtained, and the exponential convergence rate is estimated. In the last part, the exponential stability of string of vehicle in automatic vehicle following systems is studied, based on the new results for the exponential stability of string of vehicle, applying sliding mode control method, the longitudinal control laws for each vehicle in the platoon are designed and the longitudinal following controllers are constructed. From the simulation of the platoon, convergence rate of spacing errors and velocity errors of the vehicle platoon is fast. Since the criteria of the stability of the above three classes of interconnected large-scale systems with time delays are independent of the delays, it is easy to test the conditions of the criteria in practice.