the control law (3) does not only improves the transient performance, but also provides smoother outputs. It is important to stress that a better performance can still be achieved with (28) and (30). However, as discussed in Remark IV.1, increasing gains would not only cause more peaks in the outputs, but it might also yield saturation, especially for 2. V. CONCLUSION The tracking control probl...

in this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (hoamsc). it is proved that the proposed controller is robust to m...

In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...

This paper presents a new observer that estimates the exact state of a linear continuous-time system in predetermined finite time. The finite convergence time of the proposed observer is achieved by updating the observer state based on the difference between the measured output and the estimated output at discrete time instants. Simulation results are presented to illustrate the convergence beh...

If at each point of a set of positive Lebesgue measure, every rearrangement of a multiple trigonometric series square converges to a finite value, then that series is the Fourier series of a function to which it converges uniformly. If there is at least one point at which every rearrangement of a multiple Walsh series square converges to a finite value, then that series is the Walsh-Fourier ser...

In this paper, we study finite-time convergence of gossip algorithms. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists a globally finite-time convergent gossip algorithm despite the number of nodes if asymmetric gossiping is allowed. For n = 2 nodes, we prove that a fastes...

Motivated by the design of observers with good performance and robustness to measurement noise, the problem of estimating the state of a linear time-invariant system in finite time and robustly with respect to measurement noise is considered. Using a hybrid systems framework, a hybrid observer producing an estimate that converges to the plant state in finite time, even under unknown piecewise-c...

In this paper an Adaptive Continuous Twisting Algorithm (ACTA) is presented. For double integrator, ACTA produces a continuous control signal ensuring finite time convergence of the states to zero. Moreover, the control signal generated by ACTA, compensates the Lipschitz perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. ACTA also keeps its converge...