Numerical Integrator based on Implicit Euler Discretization of Twisting Control Algorithm

In this paper, an implicit discrete-time version of the integrator based on the twisting control algorithm is proposed. In the noise-free cases, the integrator converges exactly to the integration of the signal in finite time. In the noisy cases, the numerical chattering has been suppressed. The values of the control input are obtained by using the framework of variational inequalities and linear complementary problems. Lyapunov functions are used to guarantee convergence of the proposed integrator. The methodology is illustrated by simulation results. Moreover, the proposed design is compared with other classical integration techniques such as the composite trapezoidal, composite Simpson's rule and composite Runge-Kutta fourth-order method.