Direct adaptive control design for reachable linear discrete-time uncertain systems

In this paper, we develop a direct adaptive control framework for MIMO linear uncertain systems. The proposed adaptive controller addresses adaptive stabilization while under the reachability assumption. The method can be easily extended to the system with bounded exogenous disturbances and ℓ₂ disturbances, where the disturbance rejection can be addressed. The framework is Lyapunov-based and the adaptive laws are characterized by Kronecker calculus. Finally, several numerical examples are provided to demonstrate the efficacy of the proposed framework.