Impulsive Adaptive Control for Uncertain Linear Systems

Abstract. This paper proposes an impulsive adaptive control (IAC) law for stabilization of uncertain linear systems. Available impulsive control results are based on impulsive fixed-gain control, where the impulsive control gain is tightly coupled with the system parameters and the impulsive frequency, thus limiting the capability to tackle uncertainty. Instead of a fixed gain, the proposed control law adaptively updates the gain at impulsive instants. The fact that adaptation occurs at discrete time instants can result in a more practical implementation as compared to IAC with continuous-time adaptation, i.e., requiring one to solve adaptive equations in a continuous fashion. Stability conditions for the proposed IAC protocol are established, showing less conservatism than impulsive fixed-gain control and more capability to handle uncertainties in the system and in the impulsive frequency. Numerical comparisons further verify the effectiveness of the proposed IAC scheme.