Unconditional stabilization of linear discrete systems via adaptive control

Abstract

This paper deals with the conditions of overall deterministic stability of the adaptive control schemes which may be obtained by associating any usual identification and control methods (e.g. Recursive Minimum Square, Stochastic Approximation, Extended Kalman Filter, for Identification; Model Reference, Pole Placement, Quadratic Optimization, for Control). The deterministic and time invariance hypotheses are introduced here only for the analysis of the above schemes, but not for their synthesis. There are no assumptions of sufficiently exciting input, or any requirement for parameter convergence, nor an hypothesis of bounded input and output signals.