On the improvement of linear discrete system stability: the maximal set of the \(F\)-admissible initial states (Q1768074)

A discrete linear control system is considered under the assumption that its output is stabilizable by a given state-feedback control law. The author characterizes the set of all initial states \(x_0\) for which the output function \(y(i)\) of the closed-loop system satisfies the constraints \(\| y(i)\| \leq \alpha_i\), for all positive integer numbers \(i\). Here, the positive numbers \(\alpha_i\) are appropriately chosen and can be interpreted as ``a desired degree'' of stability. An algorithm for constructing this set of initial states is proposed and some numerical simulations are presented. The case of discrete-time delayed control systems is also studied.