Direct adaptive control for linear discrete-time uncertain systems with exogenous disturbances and ℓ2 disturbances

In this paper, we develop a direct adaptive control framework for MIMO linear uncertain systems with exogenous bounded disturbances and ℓ₂ disturbances. The proposed adaptive controller addresses adaptive stabilization and disturbance rejection. For bounded energy ℓ₂ disturbances the proposed method guarantees a nonexpansivity constraint on the closed-loop input-to-states map. The framework is Lyapunov-based and the adaptive laws are characterized by Kronecker calculus. The only assumption is reachability of the pair (A,B). Finally, several numerical examples are provided to demonstrate the efficacy of the proposed frameworks.