Simple adaptive and robust control for a class of time-varying systems§

Adaptive and robust control algorithms for the class of uncertain time-varying linear plants of triangular structure corrupted by disturbance are proposed in the paper. The controls are designed on the basis of pole placement approach and have only one adjustable parameter – averaged radius of roots location ω. Parameter ω is increased according to two proposed schemes until the closed-loop system becomes stable and control error exponentially decays to the neighborhood of zero equilibrium. In the first scheme parameter ω is generated by the first order adaptation algorithm, while in the second scheme this parameter is generated by nonlinear static feedback. It is shown that both control algorithms are robust in respect to disturbance and the variations of the plant parameters. The properties of designed control systems are illustrated by means of MatLab/Simulink environment.