Stabilization of Uncertain Fractional-Order Neutral-Type Delay Systems
- 1st Edition - December 1, 2025
- Latest edition
- Authors: António M. Lopes, Alireza Alfi, Zahra Sadat Aghayan
- Language: English
Stabilization of Uncertain Fractional-Order Neutral-Type Delay Systems presents an in-depth exploration of the challenges faced in stabilizing fractional-order systems with uncert… Read more
Stabilization of Uncertain Fractional-Order Neutral-Type Delay Systems presents an in-depth exploration of the challenges faced in stabilizing fractional-order systems with uncertainties, particularly those involving neutral-type delays. The book opens with a thorough introduction before advancing from constant fractional-order neutral-type systems (CFONT) to variable fractional-order counterparts (VFONT). Addressing real-world issues such as control input saturation and actuator delay, the book discusses both non-optimal and sub-optimal control approaches, including guaranteed cost controllers (GCC). It delves into output-feedback control as a viable alternative and compares static and dynamic feedback controllers, noting that dynamic controllers can enhance transient response but introduce additional complexity.
These methods ensure closed-loop system stability and performance by providing clear stabilization conditions expressed as linear matrix inequalities (LMIs), which can be efficiently solved using tools like MATLAB’s LMI toolbox or freely available software such as SEDUMI and YALMIP. Beyond theory, the book examines state- and output-feedback controller structures, acknowledging the practical limitations of accessing all system states.
These methods ensure closed-loop system stability and performance by providing clear stabilization conditions expressed as linear matrix inequalities (LMIs), which can be efficiently solved using tools like MATLAB’s LMI toolbox or freely available software such as SEDUMI and YALMIP. Beyond theory, the book examines state- and output-feedback controller structures, acknowledging the practical limitations of accessing all system states.
- Covers stability and stabilization techniques for CFONT and VFONT systems
- Presents diverse feedback control structures, including static and dynamic state- and output-feedback controllers, along with FODO for disturbance handling
- Discusses on various controllers, including non-optimal and sub-optimal (GCC), for stabilizing FONT systems
- Systematic formulation of stabilization conditions as LMIs for easy resolution using existing toolboxes, accompanied by consistent problem formulation, theoretical findings, and simulation results throughout
MSc and PhD students, as well as researchers in the fields of control and dynamical systems within applied mathematics and engineering
Part I Introduction
1 Introduction
1.1 Outline
1.2 Key challenges in control systems design
1.3 Time-delay systems representation
1.4 Delay types
1.5 Examples of time-delay systems
1.6 A brief review of stability of time-delay systems
1.7 Controller types
1.8 Fundamental concepts of fractional calculus
1.9 Fractional-order systems
1.10 Stability of fractional-order systems
1.11 Overview of the book
Part II Stabilization of constant fractional-order neutral-type delay systems Outline Basic concept Lemmas
2 Stabilization of constant fractional-order neutral-type delay systems subject to actuator saturation
2.1 Stabilization of linear constant fractional-order neutral-type delay systems with time-varying delay subject to actuator saturation
2.2 Stabilization of nonlinear constant fractional-order neutral-type delay systems with time-varying delay subject to actuator saturation
2.3 Extension of the domain of attraction
2.4 Numerical examples
3 Stabilization of constant fractional-order neutral-type delay systems with multiple delays and nonlinear perturbations subject to actuator saturation
3.1 Problem description
3.2 General assumptions
3.3 Control goals
3.4 Stabilization of the nominal system
3.5 Stabilization of systems with time-varying structured uncertainties
3.6 Extension of the domain of attraction
3.7 Numerical Examples
4 Stabilization of constant fractional-order neutral-type delay systems with distributed delays and nonlinear perturbations subject to actuator saturation
4.1 Problem description
4.2 General assumptions
4.3 Control goals
4.4 Stabilization of the nominal system
4.5 Stabilization of systems with time-varying structured uncertainties
4.6 Extension of the domain of attraction
4.7 Numerical Examples
5 Observer-based stabilization of constant fractional-order neutral-type delay systems with time-varying delay subject to actuator saturation
5.1 Problem description
5.2 General assumptions
5.3 Control goals
5.4 Stabilization of nominal system
5.5 Stabilization of uncertain systems with time-varying structured uncertainties
5.6 Extension of the domain of attraction
5.7 Numerical Examples
Part III Guaranteed-cost-based control technique for stabilization of constant fractional-order neutral-type delay systems Outline Basic concept Lemmas
6 Stabilization with time-varying structured uncertainties
6.1 Problem description
6.2 General assumptions
6.3 Control goals
6.4 Stabilization without actuator delay
6.5 Numerical examples
7 Stabilization with time-varying structured uncertainties and nonlinear perturbations
7.1 Problem description
7.2 General assumptions
7.3 Control goals
7.4 Stabilization subject to actuator delay
7.5 Numerical examples
Part IV Stability and stabilization of variable fractional-order neutral-type delay systems Outline Basic concept Lemmas
8 Stability of variable fractional-order neutral-type delay systems
8.1 Problem description
8.2 General assumptions
8.3 Stability of the nominal system
8.4 Stability of the uncertain system with time-varying structured uncertainties
8.5 Numerical examples
9 Stabilization of variable fractional-order neutral-type delay systems
9.1 Problem description
9.2 General assumptions
9.3 Control goals
9.4 Stabilization of the nominal system
9.5 Stabilization of uncertain systems with time-varying structured uncertainties
9.6 Disturbance observer-based controller design
9.7 Numerical examples Appendix A Modified Adams–Bashforth–Moulton algorithm
A.1 Numerical method References
1 Introduction
1.1 Outline
1.2 Key challenges in control systems design
1.3 Time-delay systems representation
1.4 Delay types
1.5 Examples of time-delay systems
1.6 A brief review of stability of time-delay systems
1.7 Controller types
1.8 Fundamental concepts of fractional calculus
1.9 Fractional-order systems
1.10 Stability of fractional-order systems
1.11 Overview of the book
Part II Stabilization of constant fractional-order neutral-type delay systems Outline Basic concept Lemmas
2 Stabilization of constant fractional-order neutral-type delay systems subject to actuator saturation
2.1 Stabilization of linear constant fractional-order neutral-type delay systems with time-varying delay subject to actuator saturation
2.2 Stabilization of nonlinear constant fractional-order neutral-type delay systems with time-varying delay subject to actuator saturation
2.3 Extension of the domain of attraction
2.4 Numerical examples
3 Stabilization of constant fractional-order neutral-type delay systems with multiple delays and nonlinear perturbations subject to actuator saturation
3.1 Problem description
3.2 General assumptions
3.3 Control goals
3.4 Stabilization of the nominal system
3.5 Stabilization of systems with time-varying structured uncertainties
3.6 Extension of the domain of attraction
3.7 Numerical Examples
4 Stabilization of constant fractional-order neutral-type delay systems with distributed delays and nonlinear perturbations subject to actuator saturation
4.1 Problem description
4.2 General assumptions
4.3 Control goals
4.4 Stabilization of the nominal system
4.5 Stabilization of systems with time-varying structured uncertainties
4.6 Extension of the domain of attraction
4.7 Numerical Examples
5 Observer-based stabilization of constant fractional-order neutral-type delay systems with time-varying delay subject to actuator saturation
5.1 Problem description
5.2 General assumptions
5.3 Control goals
5.4 Stabilization of nominal system
5.5 Stabilization of uncertain systems with time-varying structured uncertainties
5.6 Extension of the domain of attraction
5.7 Numerical Examples
Part III Guaranteed-cost-based control technique for stabilization of constant fractional-order neutral-type delay systems Outline Basic concept Lemmas
6 Stabilization with time-varying structured uncertainties
6.1 Problem description
6.2 General assumptions
6.3 Control goals
6.4 Stabilization without actuator delay
6.5 Numerical examples
7 Stabilization with time-varying structured uncertainties and nonlinear perturbations
7.1 Problem description
7.2 General assumptions
7.3 Control goals
7.4 Stabilization subject to actuator delay
7.5 Numerical examples
Part IV Stability and stabilization of variable fractional-order neutral-type delay systems Outline Basic concept Lemmas
8 Stability of variable fractional-order neutral-type delay systems
8.1 Problem description
8.2 General assumptions
8.3 Stability of the nominal system
8.4 Stability of the uncertain system with time-varying structured uncertainties
8.5 Numerical examples
9 Stabilization of variable fractional-order neutral-type delay systems
9.1 Problem description
9.2 General assumptions
9.3 Control goals
9.4 Stabilization of the nominal system
9.5 Stabilization of uncertain systems with time-varying structured uncertainties
9.6 Disturbance observer-based controller design
9.7 Numerical examples Appendix A Modified Adams–Bashforth–Moulton algorithm
A.1 Numerical method References
- Edition: 1
- Latest edition
- Published: December 1, 2025
- Language: English
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António M. Lopes
António M. Lopes received a PhD in Mechanical Engineering in 2000, from the University of Porto, Portugal. His current research interests are: Automation, Robotics, Complex Systems, Fractional Order Systems, Modelling and Control.
Affiliations and expertise
Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Porto, PortugalAA
Alireza Alfi
Alireza Alfi received a PhD in Control Engineering in 2008, from the Iran University of Science and Technology, Tehran, Iran. His current research interests are: Control Systems Theory, Time Delay Systems, Fractional Order Systems, Multi-agent Systems, Optimization.
Affiliations and expertise
Faculty of Electrical Engineering, Shahrood University of Technology, Shahrood, IranZA
Zahra Sadat Aghayan
Zahra Sadat Aghayan received a PhD in Control Engineering in 2021, from the Shahrood University of Technology, Shahrood, Iran. Her current research interests are: Fractional Order Systems, Time Delay Systems, Robust Control, Linear Matrix Inequalities.
Affiliations and expertise
Electrical Engineering Department, Faculty of Engineering, University of Garmsar, Iran