Adaptive stabilizability and robustness under the presence of unmodeled dynamics of non necessarily controllable continuous-time systems

Presents an indirect adaptive control scheme which is applicable to continuous linear time-invariant systems of unknown parameters even if the plant is not inversely stable. The scheme is a pole-placement type while leading to performances very close to those of model-following schemes without requiring the plant inverse stability assumption. The control objective is that the plant output should asymptotically track the reference signal given by an arbitrary stable filter under a small stationary tracking-error in some prefired frequency interval while ensuring robust closed-loop stability. The adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics, and possibly bounded disturbances, are proved without assuming the controllability of the modeled plant. The control is designed such that the steady-state tracking be perfect, for the chosen frequency range, in the ideal case of a known plant. A normalized least-squares algorithm with a relative adaptation dead-zone and `a posteriori´ modification of the parameter estimates is used to update the plant parameters in the adaptive case. The relative adaptation dead-zone is included for robustness purposes and the modification is crucial to obtain a controllable estimated model of the plant for all time and at the limit