On the adaptive stabilization of linear time-varying systems

In this paper we are concerned with the adaptive stabilization of linear time-varying (LTV) plants with reduced prior knowledge. We consider the standard feed back control configuration (2.3.a) where the compensator has fixed poles and the numerator coefficients are updated on-line. Assuming stabilizability (possibly with a time-varying controller) of the plant, it is shown that the adaptive controller insures boundedness of all signals if: i) the rate of variation of the parameters of the plant in closed loop with a stabilizing controller is small; ii) the "gain" of the later closed loop plant is small and iii) adaptation is slow. No assumption regarding the plants order, relative degree or stable invertibility are imposed, neither we rely on persistency of excitation or projection arguments.