By simple computations and the applications of Theorem 4.2 we obtain the following lemmas.
Then, by a simple computation and by using the fact that (2.15).
When (alpha=1), (beta=1), and (gamma=0.5), by simple computation, we have delta=frac{alpha+beta M}{alpha+beta M-gamma}=1.25, and so rtheta-lndeltaapprox-0.0731< 0, that is, the condition of Theorem 3.1 holds.
By simple computation, we obtain (0< Lleq{1.9092}), choose (L=1.5), (delta=1), (p=2), and then the conditions (J1) and (J2) are satisfied.
Therefore, the positive numbers and in (2.6) and (2.10) can be taken as, and the results can be obtained by simple computation.
Key features of our method, that combines hybrid control with Model Predictive Control (MPC) techniques, are the possibility to take into account input constraints in order to plan the sensing maneuver and the ability of the followers to detect containment violations by simple computation based on the available information about the leaders' positions.
By simple computation, we have.
By simple computation, we obtain (zeta_< Pi ).
By simple computation, we know that (2.16).
