Sentence examples for bounded in the square from inspiring English sources

Furthermore, note that k is continuous (and therefore bounded) in the square ([0,1] times [0,1]) and that its partial derivatives (frac{partial k}{partial t}) and (frac{partial k}{partial s}) can be discontinuous on the diagonal (t=s).

The purpose of this problem is to design a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square.

The purpose of this problem is to design a state feedback controller such that the closed-loop system is exponentially stable (or exponentially ultimately bounded) in the mean square, for all admissible nonlinearities and time-delays.

We aim at designing a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically, exponentially, ultimately bounded in the mean square, for all admissible nonlinearities and time delays.

It occupies an area of 2,434 square miles (6,304 square km) and is bounded in the north by Ukraine.

Using Itˆo formula and Chebyshev's inequality, it is shown that all the signals in the closed-loop system are bounded in probability, and the error signals are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment.

The design objective is to make the error system uniformly ultimately bounded in mean square.

Based on the estimation value, a disturbance observer based attenuation and rejection controller is constructed such that the closed-loop system is asymptotically bounded in mean square or asymptotically stable in probability under different conditions.

The proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square.

Analysis results were developed for the stability bounds in the mean and mean-square sense.

By constructing a new Lyapunov Krasovskii (L K) functional and modifying the adding a power integrator method, an output tracking controller is well designed such that all signals of the closed-loop system are bounded in probability and the mean square of the tracking error can be adjusted as small as possible.