Robust direct adaptive feedback control for linear discrete-time uncertain systems

In this paper, we developed a direct adaptive control framework for the linear discrete-time uncertain MIMO systems, with the assumptions on controllability of the system and the difference of the unknown system matrix from the stable solution is bounded by given value. The proposed framework is Lyapunov-based and the controller guarantees adaptive stabilization. In addition, the adaptive laws are characterized by Kronecker calculus. Furthermore, the results can easily extended to time-varying cases where the deviation from the stable solution is bounded, and the controllability assumption hold. The controller not only can tolerate plant deviation, but also guarantees asymptotically stable of the closed-loop system. Two numerical examples are provided for performance demonstration.