Stability of implicit self-tuning controllers for time-varying systems based on Lyapunov function.

• Anna Patete Universidad de Los Andes-Venezuela
• Katsuhisa Furuta Tokyo Denki University

Palabras clave: self-tuning control, generalized minimum variance control, sliding-mode control, discrete-time systems, time-varying systems, Lyapunov function

Resumen

The important issue on self-tuning control includes the stability, performance and convergence of involved recursive algorithms. Based on a Lyapunov function, this paper proves the stability of implicit self-tuning controllers, combining recursive parameters estimation with a forgetting factor and generalized minimum variance criterion, for time-varying systems. The system parameters are considered to be changing continuously but slowly or changing abruptly but infrequently. The analysis is extended to the case where the system model is subject to system and measurement noises. The main results are the theorems which assure the overall stability of the closed-loop system, which are proved in a straight way com- pared with previous stability analysis results.