Admissible Control for Non-Linear Singular Systems Subject to Time-Varying Delay and Actuator Saturation: An Interval Type-2 Fuzzy Approach

Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when...

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Bibliographic Details
Published inActuators Vol. 12; no. 1; p. 30
Main Authors Kchaou, Mourad, Regaieg, Mohamed Amine, Jerbi, Houssem, Abbassi, Rabeh, Stefanoiu, Dan, Popescu, Dumitru
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2023
Subjects
actuator saturation
Actuators
Closed loops
Constraint modelling
Control systems
Controllers
Delay
Feedback control
Fuzzy control
Fuzzy sets
IT-2 fuzzy model
Linear matrix inequalities
Literature reviews
Mathematical analysis
Nonlinear control
Nonlinear systems
Optimization
R&D
Research & development
Saturation
singular system
State feedback
Systems stability
time varying delay
Uncertainty
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Summary:Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when uncertainty also simultaneously affects the system under consideration. To address this issue, this paper investigated a feasible control strategy for nonlinear singular systems with time-varying delay that are subject to uncertainty and actuator saturation. The IT-2 fuzzy model was adopted to describe the dynamic of the non-linear delayed systems using lower and upper membership functions to deal with the uncertainty. Moreover, the polyhedron model was applied to characterize the saturation function. The goal of the control approach was to design a relevant IT2 fuzzy state feedback controller with mismatched membership functions so that the closed-loop system is admissible. On the basis of an appropriate Lyapunov–Krasovskii functional, sufficient delay-dependent conditions were established and an optimization problem was formulated in terms of linear matrix inequality constraints to optimize the attraction domain. Simulation examples are provided to verify the effectiveness of the proposed method.
ISSN:2076-0825
2076-0825
DOI:10.3390/act12010030