LMI-based stability analysis of fractional order systems of neutral type with time varying delays under actuator saturation

Aghayan, Zahra Sadat; Alfi, Alireza; Machado, J. A. Tenreiro

doi:10.1007/s40314-021-01522-6

Cited by 15 publications

(7 citation statements)

References 54 publications

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“…For given positive numbers c 1 , c 2 , T (c 2 ≥ c 1 ). Consider the system (1) and the cost function (1). If there exists a state feedback control u * (t) and a positive constant J * such that the closed-loop system (4) is robustly finite-time stable (c 1 , c 2 , T) and the closed-loop value of the cost function satisfies J ≤ J * , then the value J * is called guaranteed-cost.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Fractional‐order systems (FOs) and fractional calculus have become hot research topics in science and engineering due to various applications of FOs in real‐life problems. During the last decades, many important results on FOs have been explored and various issues have been studied by many researchers, such as asymptotic stability, 1 passivity and passification performances, 2 dissipativity analysis, 3 extended dissipativity, 4 hopf bifurcation analysis 5 . In recent years, the guaranteed cost control (GCC) problem of FOs has received much attention due to its both theoretical and practical importance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

Thành

Thuận

Tuan

2023

Optim Control Appl Methods

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This article deals with the problem of finite time guaranteed cost control for uncertain polytopic fractional‐order systems with time‐varying delays. A linear quadratic cost function is considered as a performance measure for the closed‐loop system. By using Laplace transform and linear matrix inequalities (LMIs), a guaranteed cost controller design is presented and sufficient conditions for the existence of a finite time guaranteed cost state‐feedback control for the system are given in terms of LMIs. Two numerical examples are given to illustrate the effectiveness of the obtained result.

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Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

Thành

Thuận

Tuan

2023

Optim Control Appl Methods

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“…Although a well consolidated area, there are, however, still numerous open problems and paths to be unraveled [14][15][16][17]. A research path that some mathematicians have recently been interested consists to investigate fractional calculus on time scales [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness, and controllability for Hilfer differential equations on times scales

Sousa

Oliveira

Frederico

et al. 2023

Math Methods in App Sciences

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We introduce a new version of ψ$$ \psi $$‐Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated, and in particular, we prove an integration by parts formula. Using the Laplace transform and the obtained integration by parts formula, we then propose a ψ$$ \psi $$‐Riemann–Liouville fractional integral on times scales. The applicability of the new operators is illustrated by considering a fractional initial value problem on an arbitrary time scale, for which we prove existence, uniqueness, and controllability of solutions in a suitable Banach space. The obtained results are interesting and nontrivial even for the following particular choices: (i) of the time scale, (ii) of the order of differentiation, and/or (iii) function ψ$$ \psi $$, opening new directions of investigation. Finally, we end the article with comments and future work.

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“…FO neutral-type delay systems are more general than other types of delayed systems [ 27 ]. Thus, the stabilization of such systems for both integer- [ 28 , 29 ] and fractional-order [ 30 , 31 , 32 , 33 , 34 ] systems is a challenging topic. In the real world, mechanical and electrical components can cause a time delay in actuators.…”

Section: Introductionmentioning

confidence: 99%

“…A great deal of works reporting on the stability of neutral systems adopted a state-feedback controller [ 31 , 32 , 33 , 34 , 51 , 52 ]. However, it is possible that not all the system’s states are accessible.…”

Section: Introductionmentioning

confidence: 99%

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

Aghayan

Alfi

Lopes

2022

Entropy

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In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov’s theory. Two application examples verify the analytic findings.

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LMI-based stability analysis of fractional order systems of neutral type with time varying delays under actuator saturation

Cited by 15 publications

References 54 publications

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

Existence, uniqueness, and controllability for Hilfer differential equations on times scales

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

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