All Stories

  1. Hybrid Particle Swarm and Grey Wolf Optimization for Robust Feedback Control of Nonlinear Systems

    Article • Automation, December 2025, MDPI AG

    PhD. Robert Vrabel

  2. Hybrid Particle Swarm and Grey Wolf Optimization for Robust Feedback Control of Nonlinear Systems

    Article • November 2025, MDPI AG

    PhD. Robert Vrabel

  3. Optimum settings for discrete PID control of nonlinear systems

    Article • Swarm and Evolutionary Computation, August 2025, Elsevier

    PhD. Robert Vrabel

  4. (Iq)–Stability and Uniform Convergence of the Solutions of Singularly Perturbed Boundary Value Problems

    Article • Mathematics, June 2023, MDPI AG

    PhD. Robert Vrabel

  5. Lower and Upper Solution Method for Semilinear, Quasi-Linear and Quadratic Singularly Perturbed Neumann Boundary Value Problems

    Article • Axioms, February 2023, MDPI AG

    PhD. Robert Vrabel

  6. A novel criterion for global incremental stability of dynamical systems

    Article • Communications in Nonlinear Science and Numerical Simulation, November 2022, Elsevier

    PhD. Robert Vrabel

  7. On One Problem of the Nonlinear Convex Optimization

    Article • AppliedMath, September 2022, MDPI AG

    PhD. Robert Vrabel

  8. Non-Resonant Non-Hyperbolic Singularly Perturbed Neumann Problem

    Article • Axioms, August 2022, MDPI AG

    PhD. Robert Vrabel

  9. Quasi-Density of Sets, Quasi-Statistical Convergence and the Matrix Summability Method

    Article • Axioms, February 2022, MDPI AG

    PhD. Robert Vrabel

  10. When Is σ (A(t)) ⊂ {z ∈ ℂ; ℜz ≤ −α < 0} the Sufficient Condition for Uniform Asymptotic Stability of LTV System ẋ = A(t)x?

    Article • Mathematics, January 2022, MDPI AG

    PhD. Robert Vrabel

  11. Note on F-Graph Construction

    Article • Computation, June 2021, MDPI AG

    PhD. Robert Vrabel

  12. Design of the State Feedback-Based Feed-Forward Controller Asymptotically Stabilizing the Overhead Crane at the Desired End Position

    Article • Journal of Applied Nonlinear Dynamics, June 2021, L&H Scientific Publishing, LLC

    PhD. Robert Vrabel

  13. Criterion for robustness of global asymptotic stability to external perturbations of linear time-varying systems

    Article • International Journal of General Systems, January 2021, Taylor & Francis

    PhD. Robert Vrabel

  14. Logarithmic norm based robust adaptive state‐feedback control of the linear time‐varying systems under system uncertainty and external disturbances

    Article • Advanced Control for Applications, November 2020, Wiley

    PhD. Robert Vrabel

  15. Design of the state feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type overhead cranes with time-varying hoisting rope length

    Article • International Journal of Nonlinear Sciences and Numerical Simulation, October 2020, De Gruyter

    PhD. Robert Vrabel

  16. Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

    Article • Mathematics, June 2020, MDPI AG

    PhD. Robert Vrabel

  17. A Note on Uniform Exponential Stability of Linear Periodic Time-Varying Systems

    Article • IEEE Transactions on Automatic Control, April 2020, Institute of Electrical & Electronics Engineers (IEEE)

    PhD. Robert Vrabel

  18. Asymptotic stabilization of a system of coupled $${\varvec{n}}$$th-order differential equations with potentially unbounded high-frequency oscillating perturbations

    Article • Nonlinear Dynamics, March 2020, Springer Science + Business Media

    PhD. Robert Vrabel

  19. Logarithmic norm-based analysis of robust asymptotic stability of nonlinear dynamical systems

    Article • Communications in Nonlinear Science and Numerical Simulation, January 2020, Elsevier

    PhD. Robert Vrabel

  20. Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems

    Article • Symmetry, April 2019, MDPI AG

    PhD. Robert Vrabel

  21. On local asymptotic stabilization of the nonlinear systems with time-varying perturbations by state-feedback control

    Article • International Journal of General Systems, November 2018, Taylor & Francis

    PhD. Robert Vrabel

  22. Local null controllability of the control-affine nonlinear systems with time-varying disturbances

    Article • European Journal of Control, March 2018, Elsevier

    PhD. Robert Vrabel

  23. GENERALIZED MATRIX DETERMINANT LEMMA AND THE CONTROLLABILITY OF SINGLE INPUT CONTROL SYSTEMS

    Article • International Journal of Pure and Apllied Mathematics, September 2017, Academic Publications

    PhD. Robert Vrabel

  24. Stabilisation and state trajectory tracking problem for nonlinear control systems in the presence of disturbances

    Article • International Journal of Control, August 2017, Taylor & Francis

    PhD. Robert Vrabel

  25. Numerical Investigation of Initial Condition and Singular Perturbation Parameter Value Influence on the Dynamical System Oscillatory Behaviour

    Article • September 2016, Institute of Electrical & Electronics Engineers (IEEE)

    PhD. Robert Vrabel

  26. Formation of boundary layers for singularly perturbed fourth-order ordinary differential equations with the Lidstone boundary conditions

    Article • Journal of Mathematical Analysis and Applications, August 2016, Elsevier

    PhD. Robert Vrabel

  27. Influence of selected parameters on oscillatory behaviour of dynamical system

    Article • International Journal of Mathematical Analysis, January 2016, Hikari, Ltd.

    PhD. Robert Vrabel

  28. Mathematical Approach to Security Risk Assessment

    Article • Mathematical Problems in Engineering, January 2015, Hindawi Publishing Corporation

    PhD. Robert Vrabel

  29. Numerical simulation of high sensitivity of solutions to the nonlinear singularly perturbed dynamical system on the initial conditions and parameter

    Article • International Journal of Mathematical Analysis, January 2015, Hikari, Ltd.

    PhD. Robert Vrabel

  30. On the lower and upper solutions method for the problem of elastic beam with hinged ends

    Article • Journal of Mathematical Analysis and Applications, January 2015, Elsevier

    PhD. Robert Vrabel

  31. Remark on the sensitivity of simulated solutions of the nonlinear dynamical system to the used numerical method

    Article • International Journal of Mathematical Analysis, January 2015, Hikari, Ltd.

    PhD. Robert Vrabel

  32. A Heat Transfer Approach to the Calculation of Residual Power of Used Nuclear Fuel

    Article • Nuclear Technology, February 2014, Taylor & Francis

    PhD. Robert Vrabel

  33. Active Control of Oscillation Patterns in the Presence of Multiarmed Pitchfork Structure of the Critical Manifold of Singularly Perturbed System

    Article • Mathematical Problems in Engineering, January 2013, Hindawi Publishing Corporation

    PhD. Robert Vrabel

  34. Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control

    Article • Abstract and Applied Analysis, January 2013, Hindawi Publishing Corporation

    PhD. Robert Vrabel

  35. Turning point analysis of the concave steady-state solutions for nonlinear singularly perturbed heat transfer equation

    Article • International Journal of Mathematical Analysis, January 2013, Hikari, Ltd.

    PhD. Robert Vrabel

  36. Estimation of Turning Point Location of Convex Solutions for Nonlinear Second-Order Differential Equations

    Article • Mathematical Modelling and Analysis, November 2012, Vilnius Gediminas Technical University

    PhD. Robert Vrabel

  37. Simulation of Geometric Approach to the Study of Singularly Perturbed Differential Equations Using Matlab

    Article • August 2012, Institute of Electrical & Electronics Engineers (IEEE)

    PhD. Robert Vrabel

  38. On the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems

    Article • Systems & Control Letters, March 2012, Elsevier

    PhD. Robert Vrabel

  39. Frequency control of singularly perturbed forced duffing’s oscillator

    Article • Journal of Dynamical and Control Systems, July 2011, Springer Science + Business Media

    PhD. Robert Vrabel

  40. Nonlocal Four-Point Boundary Value Problem for the Singularly Perturbed Semilinear Differential Equations

    Article • Boundary Value Problems, January 2011, Springer Science + Business Media

    PhD. Robert Vrabel

  41. Singularly perturbed anharmonic quartic potential oscillator problem

    Article • Zeitschrift für angewandte Mathematik und Physik, July 2004, Springer Science + Business Media

    PhD. Robert Vrabel

  42. Semilinear singular perturbation

    Article • Nonlinear Analysis, July 1995, Elsevier

    PhD. Robert Vrabel