Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Feedback control systems01:26

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Control Systems01:10

Control Systems

Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
At the heart...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Effects of feedback01:24

Effects of feedback

Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Open and closed-loop control systems01:17

Open and closed-loop control systems

Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal and...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Mixed Control Strategy for a Class of Sector-Bounded Nonlinear Systems.

Entropy (Basel, Switzerland)·2025
Same author

Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities.

Entropy (Basel, Switzerland)·2024
Same author

L∞ analysis and state-feedback control of Hopfield networks.

IEEE transactions on neural networks and learning systems·2014
See all related articles

Related Experiment Video

Updated: May 28, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

State Feedback Optimal L2-Induced Control of Nonlinear Systems Utilizing Universal Approximation.

Adrian-Mihail Stoica1, Isaac Yaesh2

  • 1Faculty of Aerospace Engineering, National University of Science and Technology POLITEHNICA of Bucharest, 011061 Bucharest, Romania.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary

This study introduces an optimal L2-induced control method for systems with multiple nonlinearities. The approach uses linear matrix inequalities (LMIs) to ensure system stability and performance.

Keywords:
L2-induced norm boundedness conditionsconservatism reductionsector-bounded nonlinearitiesstate feedback controluniversal approximation theoremvan der Pol forced oscillator

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Related Experiment Videos

Last Updated: May 28, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Control Theory
  • Nonlinear Systems Analysis
  • Optimization Techniques

Background:

  • Systems with multiple sector-bounded nonlinearities pose challenges for traditional control design.
  • Ensuring boundedness of the L2-induced norm is crucial for stability and performance guarantees.
  • Existing methods often struggle to handle complex nonlinearities effectively.

Purpose of the Study:

  • To develop an optimal L2-induced control strategy for systems featuring multiple sector-bounded nonlinearities.
  • To derive sufficient conditions for L2-induced norm boundedness using linear matrix inequalities (LMIs).
  • To formulate and solve the optimal state feedback control problem for this class of systems.

Main Methods:

  • Derivation of sufficient boundedness conditions for the L2-induced norm using a system of LMIs.
  • Formulation and solution of an optimal state feedback control problem based on the derived LMI conditions.
  • Development of a procedure to reduce the conservatism of the obtained conditions.
  • Application of the universal approximation theorem to represent broader classes of nonlinearities using sector-bounded sigmoid functions.

Main Results:

  • Sufficient conditions for L2-induced norm boundedness were established using LMIs.
  • An optimal state feedback controller was designed and validated for systems with multiple sector-bounded nonlinearities.
  • A method to reduce conservatism in the derived conditions was successfully implemented.
  • The proposed formulation demonstrated applicability to a wider range of nonlinearities, including those approximated by sigmoid functions.

Conclusions:

  • The presented optimal L2-induced control approach effectively addresses systems with multiple sector-bounded nonlinearities.
  • The use of LMIs provides a systematic way to ensure stability and performance.
  • The method's flexibility, enhanced by the universal approximation theorem, broadens its applicability to complex nonlinear systems.
  • Numerical validation on a van der Pol oscillator confirms the theoretical developments.