New Versions of Halanay’s Inequality With Multiple Gain Terms

High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains

“…Remark 1: The condition (23), which refers to the hypothesis related to the constant bound, has been introduced in [24]. It assumes that the time-varying features of α 2 (t) and β(t) parameters are implicitly removed.…”

“…Indeed, this condition is tailored to the analysis of the high-gain observer-like design leading to essentially rejecting the measurement noise and reducing the peaking. Additionally, this condition (23) on ε is required to ensure the exponential convergence to zero of ē(t), according to (26).…”

Event-triggered control for discrete-time delay systems

“…Remark 2. Compared with the recent result in [23], Lemma 1 has the following advantages. Lemma 1 requires a > b and then the parameter α in the triggering condition can be selected so that a − b > α.…”

“…Lemma 1 requires a > b and then the parameter α in the triggering condition can be selected so that a − b > α. However, the result in [23] requires a > be ar , that is, the maximum involved delay r is upper bounded by 1 a ln(a/b). Therefore, Lemma 1 can be applied to systems with any bounded time delays, while the result in [23] is only applicable to systems with time delays smaller than 1 a ln(a/b).…”

“…However, the result in [23] requires a > be ar , that is, the maximum involved delay r is upper bounded by 1 a ln(a/b). Therefore, Lemma 1 can be applied to systems with any bounded time delays, while the result in [23] is only applicable to systems with time delays smaller than 1 a ln(a/b). Furthermore, the exponential convergence rate η can be derived explicitly by solving the unique solution of the equation in Lemma 1 and then comparing it with parameter β in (5).…”