Stability Analysis of a Linear Parameter Varying Adaptive Output Feedback Control System

Output feedback control systems often require an adaptive filter for properly shaping the loop transfer function, as certain system plant parameters may be uncertain or varying. This renders the overall closed loop to a linear parameter varying (LPV) system, for which the stability analysis is challenging due to non-trivial dynamics of the adaptation law. This paper develops a stability analysis technique of a feedback controlled oscillatory system. A polytopic overapproximation of the parameter set together with the feasibility of certain LMIs guarantees asymptotic stability of the closed loop. The varying filter parameter is only required to be lower and upper bounded, where the admissible bounds can be obtained from the proposed strategy. Hence, any filter adaptation law is allowed for this parameter range. A meaningful numerical example based 011 a fifth-order plant and a second-order adaptive filter demonstrates the usefulness and appealing simplicity of the proposed approach.