Stable adaptive control with parameter schedulings for time-varying delay systems

The stability problem of an adaptive control with parameter schedulings for time-varying delay systems is considered. The key to the solution of this problem lies in the design of an appropriate gradient gain in the adaptive control algorithm. Based on Lyapunov stability theory, a limit to and an optimization of the gradient gain is presented. With this selection, the adaptive control system can quickly eliminate the parameter mismatches between the process and model, such that the stability of the system is ensured. Digital and digital-analog simulations show that the resulting system operates well for different cases even when serious parameter mismatches exist