Simple Adaptive L2-gain Control for Discrete-time Systems

This paper explores the relationships between optimal ℓ2-gain control and simple adaptive control (SAC) for discrete-time systems. Namely, in the SAC scheme not only passivity and stability of the closed-loop system are considered, but it is also required that the adaptive control scheme attains some guaranteed ℓ2-gain performance. Sufficient conditions are derived for stability and asymptotic model-following of the closed-loop dynamics of the SAC scheme with a given disturbance attenuation level bound γ. These conditions are expressed in terms of bilinear matrix inequalities, which are solved using local iterations. Numerical examples are given that illustrate the method.