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pro vyhledávání: '"Vrabel, Robert"'
Autor:
Vrabel, Robert
In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability (GIS) of th
Externí odkaz:
http://arxiv.org/abs/2206.12945
Autor:
Vrabel, Robert
Publikováno v:
Advanced Control for Applications: Engineering and Industrial Systems, 2021
The conceptually new approach based on the logarithmic norm to design of robust adaptive state-feedback controller for linear time-varying (LTV) systems under system's modeling uncertainty and nonlinear external disturbance is proposed. This controll
Externí odkaz:
http://arxiv.org/abs/2007.06875
Autor:
Vrabel, Robert
Publikováno v:
Mathematics, 2020
Based on the eigenvalue idea and the time-varying weighted vector norm in state space we construct here the lower and upper bounds on the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time
Externí odkaz:
http://arxiv.org/abs/1911.03714
Autor:
Vrabel, Robert
Publikováno v:
Nonlinear Dynamics, Vol. 100, pp. 1421-1429 (2020)
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing at $x=0$
Externí odkaz:
http://arxiv.org/abs/1907.06720
Autor:
Vrabel, Robert
Publikováno v:
IEEE Transactions on Automatic Control, Volume: 65, Issue:4, On Pages: 1647-1651, 2020
In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ As a corollary, the lower and upper bounds for the Floquet characteristic exponents are established. The
Externí odkaz:
http://arxiv.org/abs/1907.04095
Autor:
Vrabel, Robert
Publikováno v:
Journal of Applied Nonlinear Dynamics, Vol. 10, No. 2, pp. 339-350, 2021
The problem of feed-forward control of overhead crane system is discussed. By combining the Kalman's controllability theory and Hartman-Grobman theorem from dynamical system theory, a linear, continuous state feedback-based feed-forward controller th
Externí odkaz:
http://arxiv.org/abs/1903.02956
Autor:
Vrabel, Robert
Publikováno v:
International Journal of General Systems, 2021
In this brief note, we establish a novel criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot x=A(t)x$ in the presence of possibly unbounded perturbations (external disturbances). To prove the result, logarithm
Externí odkaz:
http://arxiv.org/abs/1903.00873
Autor:
Vrabel, Robert
Publikováno v:
International Journal of Nonlinear Sciences and Numerical Simulation 22(6), 2021, pp. 621-639
In the present paper we focus our attention on the design of the feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type crane system with the time-varying rope length in the desired end position of payload (the ori
Externí odkaz:
http://arxiv.org/abs/1805.03882
Autor:
Vrabel, Robert
Publikováno v:
International Journal of General Systems, Volume 48 (1), pp. 80-89, 2019
In this paper, we are interested in the relation between the solutions of the control system $\dot x=f(x,u)$ and the solutions of its (potentially unknown) perturbation $\dot x=f(x,u)+w(x,t).$ Under the assumption that the linear part of the unpertur
Externí odkaz:
http://arxiv.org/abs/1802.09200
Autor:
Vrabel, Robert
Publikováno v:
European Journal of Control, Volume 40, March 2018, Pages 80-86
The problem of local null controllability for the control-affine nonlinear systems $\dot x(t)=f(x(t))+Bu(t)+w(t),$ $t\in[0,T]$ is considered in this paper. The principal requirements on the system are that the LTI pair $\left((\partial f/\partial x)(
Externí odkaz:
http://arxiv.org/abs/1709.03266