Stability and Optimal Control of Linear Systems

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Process Control and Monitoring".

Deadline for manuscript submissions: 25 July 2025 | Viewed by 730

Special Issue Editors


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Guest Editor
Instituto Federal de Educação, Ciência e Tecnologia da Bahia, Salvador, BA, Brazil
Interests: control systems theory

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Guest Editor
Department of Computer Engineering and Automation, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil
Interests: control systems theory

Special Issue Information

Dear Colleagues,

The linear dynamical systems theory is not only a cornerstone of scientific and technological advancement. The tools used to design and analyze systems and processes spanning more than a century of development and application. In particular, due to the superposition property of the solutions, the field of control systems benefits from the simplicity and unification of approaches and techniques that provide stable, robust, or even safe controllers to stabilize and deliver the closed-loop performance prescribed to the plant. From industrial applications to flight control and from cruise control to biomedical systems and artificial organs, linear system tools can be applied to these tasks, even when nonlinear behavior governs the system’s dynamics. Two main characteristics are paramount when the designer applies linear dynamical systems techniques: closed-loop system stability—at least on the local/regional level—and optimal performance—fast transient response and robustness, among others. This Special Issue aims to publish contributions covering topics related to the stability and optimal control of linear systems, including the following:

  • LMI-based design techniques;
  • Frequency-domain-based design techniques;
  • Linearization approaches—such as feedback linearization and multi-model/switched controllers;
  • Data-driven control and identification of linear systems;
  • Control of linear systems with dead time/time delays;
  • Model or controller order reduction;
  • Model-based predictive control;
  • Optimal control—such as LQR, LQG—and applications;
  • The control of mechatronic/multibody/vibratory systems;
  • The control of applications in industrial environments.

Contributions highlighting theoretical developments, case studies, and improvements on previously established results are welcome to be submitted to the editorial workflow and may be published after rigorous peer review.

Prof. Dr. José Mario Araújo
Prof. Dr. Carlos Eduardo Trabuco Dórea
Guest Editors

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Keywords

  • linear systems
  • stability
  • optimization
  • control
  • filtering

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Published Papers (1 paper)

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Research

11 pages, 1220 KiB  
Article
Mean Square Stability and Stabilization for Linear Parabolic Stochastic Partial Difference Systems
by Shangyu Yong, Xisheng Dai, Tao Luo and Zhengcui Wang
Processes 2025, 13(4), 1175; https://doi.org/10.3390/pr13041175 - 13 Apr 2025
Viewed by 205
Abstract
This paper studies the mean square stability and stabilization of linear parabolic stochastic partial difference systems, which contain space–time characteristics and stochastic noise. A definition of the mean square stability for this system is proposed. Using stochastic analysis and some mathematical analysis methods, [...] Read more.
This paper studies the mean square stability and stabilization of linear parabolic stochastic partial difference systems, which contain space–time characteristics and stochastic noise. A definition of the mean square stability for this system is proposed. Using stochastic analysis and some mathematical analysis methods, a strict decreasing sequence is constructed to represent the expectation of the sum of squares of the state variable along the spatial dimension. The sufficient conditions of the mean square stability are established based on system parameters, and then the convergence along the time axis is rigorously proven by the Squeeze criterion. Moreover, some stabilization criteria are derived by designing a linear feedback controller. Finally, two examples are given to illustrate the effectiveness of the results. Full article
(This article belongs to the Special Issue Stability and Optimal Control of Linear Systems)
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