Uncertain discrete systems: uniform ultimate bounded stabilization

Input‐based event‐triggered control of a discrete‐time singularly perturbed system under a resource constrained environment

“…Definition The solutions of $$$ \zeta \left(k+1\right)=f\left(\zeta \right) $$$ are called uniformly ultimately bounded to a set ( $$$ \omega $$$), if for each initial condition $$$ {\zeta}_0\in {\mathrm{\mathbb{R}}}^n $$$, there exists a time $$$ T\left({\zeta}_0\right)\ge 0 $$$ such that any state trajectory of the system with initial condition $$$ {\zeta}_0 $$$ satisfies $$$ \zeta (k)\in \omega $$$, $$$ \forall k\ge T\left({\zeta}_0\right) $$$ [49]. …”

“…Definition 3. The solutions of 𝜁 (k + 1) = 𝑓 (𝜁 ) are called uniformly ultimately bounded to a set (𝜔), if for each initial condition 𝜁 0 ∈ R n , there exists a time T(𝜁 0 ) ≥ 0 such that any state trajectory of the system with initial condition 𝜁 0 satisfies 𝜁(k) ∈ 𝜔, ∀k ≥ T(𝜁 0 ) [49].…”