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Mathematics
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Robust Stabilization of Linear and Nonlinear Systems
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Robust Stabilization of Linear and Nonlinear Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (20 January 2021) | Viewed by 6919

Special Issue Editors

Prof. Dr. Peter Benner

E-Mail Website
Guest Editor
Computational Methods in Systems and Control Theory Group, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
Interests: numerical linear algebra; numerical methods for control system design; model reduction and system approximation
Prof. Dr. Jan Heiland

E-Mail Website
Guest Editor
Computational Methods in Systems and Control Theory Group, Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany
Interests: stabilization; robust control; optimization; differential–algebraic equations; Navier–Stokes equations; simulation; model order reduction

Special Issue Information

Dear Colleagues,

Robust stabilization is a classical topic in the mathematical system theory and is concerned with ensuring the stability of a system that is robust against structured or unstructured perturbations. The investigation of robustly stabilizing controllers has brought numerous interesting theoretical results and has helped us to master many challenging problems in simulation, experiments, and every day use. Still, the field is wide open for related and relevant mathematical research and engineering applications.

In this Special Issue, we shall collect recent theoretical and application directed advances regarding the robust stabilization of linear and nonlinear systems. This includes and is not limited to feedback control, infinite-dimensional systems, PDEs, large-scale systems, quadratic or bilinear systems, input-affine systems, general nonlinear systems, or numerical methods for robust controller design.

Prof. Dr. Peter Benner
Prof. Dr. Jan Heiland
Guest Editors

Manuscript Submission Information

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Keywords

  • Robust control
  • Stabilization
  • Linear systems
  • Nonlinear systems

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Published Papers (3 papers)

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Research

19 pages, 769 KiB  
Article
Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept
by Pedro Zamora, Alejandro Arceo, Noé Martínez, Gerardo Romero and Luis E. Garza
Mathematics 2021, 9(4), 429; https://doi.org/10.3390/math9040429 - 22 Feb 2021
Cited by 4 | Viewed by 1724
Abstract
This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to [...] Read more.
This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials. Full article
(This article belongs to the Special Issue Robust Stabilization of Linear and Nonlinear Systems)
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12 pages, 1640 KiB  
Article
Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity
by Chih-Hsueh Lin, Guo-Hsin Hu and Jun-Juh Yan
Mathematics 2020, 8(3), 327; https://doi.org/10.3390/math8030327 - 3 Mar 2020
Cited by 7 | Viewed by 1989
Abstract
In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is [...] Read more.
In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is designed such that the controlled dynamics in the sliding manifold becomes easy to analyze. Furthermore, only by using single rippling SMC even with input nonlinearity can we ensure the existence of the sliding mode for the controlled dynamics and suppress the chaotic behavior in a manner of rippling. Under the proposed control scheme, the chaos behavior in uncertain generalized 4D Lorenz–Stenflo systems subjected to mismatched uncertainties can be robustly suppressed to predictable bounds, which is not addressed in the literature. The numerical simulation results including matched/mismatched uncertainties and nonlinear inputs are presented to verify the robustness and validity of the rippling sliding mode controller. Full article
(This article belongs to the Special Issue Robust Stabilization of Linear and Nonlinear Systems)
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12 pages, 3277 KiB  
Article
Robust Finite-Time Tracking Control for Robotic Manipulators with Time Delay Estimation
by Tie Zhang and Aimin Zhang
Mathematics 2020, 8(2), 165; https://doi.org/10.3390/math8020165 - 28 Jan 2020
Cited by 7 | Viewed by 2413
Abstract
In this study, a robust H∞ finite-time tracking controller is proposed for robotic manipulators based on time delay estimation. In this controller, there is no need to know the dynamics of robots, so it is quite simple. The high-gain observer is employed [...] Read more.
In this study, a robust H∞ finite-time tracking controller is proposed for robotic manipulators based on time delay estimation. In this controller, there is no need to know the dynamics of robots, so it is quite simple. The high-gain observer is employed to estimate the joint velocities, which makes it much lower in cost. The theorem proof shows that the closed-loop system is finite-time stable and has a L2 gain that is less than or equal to γ, which shows high accuracy and strong robustness to estimation errors and external disturbances. Simulations on a two-link robot illustrate the effectiveness and advantages of the proposed controllers. Full article
(This article belongs to the Special Issue Robust Stabilization of Linear and Nonlinear Systems)
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