TY - JOUR

T1 - Discretization of homogeneous systems using Euler method with a state-dependent step

AU - Efimov, Denis

AU - Polyakov, Andrey

AU - Aleksandrov, Alexander

PY - 2019/11

Y1 - 2019/11

N2 - Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.

AB - Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.

KW - Discretization

KW - Euler method

KW - Homogeneous systems

KW - LYAPUNOV FUNCTION

KW - DESIGN

KW - STABILITY

KW - FIXED-TIME STABILIZATION

KW - FINITE-TIME

KW - FEEDBACK

UR - http://www.scopus.com/inward/record.url?scp=85071033281&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/discretization-homogeneous-systems-using-euler-method-statedependent-step

U2 - 10.1016/j.automatica.2019.108546

DO - 10.1016/j.automatica.2019.108546

M3 - Article

AN - SCOPUS:85071033281

VL - 109

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 108546

ER -