## 7 Simulation Results
### Practical Contributions  
In this section, we highlight some of the major practical contributions of the proposed control strategy developed in this work.  
1. When theoretical results (such as those provided in the present manuscript) are taken in order to implement real-practical experiments, it is very important to know quickly if the theoretical proposed control strategy can be used for solving the stability problem or not. In this way, providing necessary and sufficient conditions for the existence of the stabilizing control strategy allows one to obtain this information immediately by making simple computations of the stated conditions. This facilitates the task of the control design for the engineers, in contrast with control strategies that are developed under heuristic methods or just present necessary or sufficient conditions.
2. In general, the time-delays phenomenon due to measurement of variables, material transportation, or teleoperation complicates the design of control strategies, however in the particular case when the size of time-delay is greater than the dominant dynamic of the system, the control design has an additional degree of complexity. This is because, under this situation, the time delay has greater adverse effects than the behavior of the controlled system when the delay time is small. As an example of this problem, there are many proposed control strategies [11; 24] that are well performed for a \"small\" time delay, but these control strategies cannot be used for controlling systems with large delay terms. This problem is illustrated and partially solved in the new version of the work; see Example 3 (Figure 15). Therefore, in this work, it is possible to control systems with greater delay size with respect to previously reported works ([11; 24]). For example, in [17], the maximum size of the delay is \(\tau<1/a-1/b_{1}+\sqrt{1/a^{2}-1/b_{1}^{2}}\) for a second order delayed system, in the present work, this bound is \(\tau<2\Big{(}1/a-1/b_{1}+\sqrt{1/a^{2}-1/b_{1}^{2}}\Big{)}\), i.e., the double of the previous delay size. This practical advantage allows the controlling of a greater variety of systems, ensuring closed-loop stability.
3. In practice, a control strategy that provides stability with respect to the uncertainties of the model is desired. These problems arise mainly from model mismatching. In this way, analytical robustness with respect to time delay is developed in Section 6. Additionally, the proposed control strategy has been evaluated via simulations on face-to-model mismatching of the process, obtaining positive results such as the preservation of closed-loop stability under the adverse mentioned condition.
4. Many industrial solutions (such as chemical engineering applications) require the regulation problem, which consists in keeping a variable at a desired value even in the presence of disturbances. In this way, the capability of a control system for tracking desired step-references and disturbance rejection is essential for solving the regulation problem. Thus, the results provided in Section 5 are related to this issue and illustrated in numerical simulations.
5. The control action and the output measurable variable performances are qualitative and quantitatively evaluated using a numerical simulation; the control action can be seen as the spent energy of the control stage to achieve the stabilization of the process, which is a very important issue from a practical viewpoint.