The causal α-exponential and the solution of fractional linear time-invariant systems

被引：1
|
作者：
Bengochea, G. [1 ,5 ]
Ortigueira, M. [2 ,3 ]
Verde-Star, L. [4 ]
机构：
[1] Univ Autonoma Ciudad Mexico, Acad Matemat, Mexico City, Mexico
[2] NOVA Univ Lisbon, UNINOVA, Lisbon, Portugal
[3] NOVA Univ Lisbon, NOVA Sch Sci & Technol, Dept Elect Engn, Lisbon, Portugal
[4] Univ Autonoma Metropolitana, Dept Matemat, Mexico City, Mexico
[5] Prol San Isidro 151, Mexico City 09790, Mexico
来源：
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE | 2024年 / 55卷 / 09期
关键词：
Fractional derivative; fractional linear systems; alpha-exponential function; impulse response; step response; NUMERICAL COMPUTATION;
D O I：
10.1080/00207721.2024.2321369
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Closed-form expressions for the impulse and step responses of commensurable linear time-invariant systems are deduced and exemplified. The algorithm is based on obtaining the solution in terms of the alpha-exponential monomials that generate a vector space containing the solutions of such systems. Several examples are considered, together with the numerical aspects involved in calculating the related series, which show the accuracy and effectiveness of the approach.
引用
收藏
页码：1790 / 1806
页数：17
相关论文
共 50 条
  • [41] On the Decidability of Reachability in Linear Time-Invariant Systems
    Fijalkow, Nathanael
    Ouaknine, Joel
    Pouly, Amaury
    Sousa-Pinto, Joao
    Worrell, James
    PROCEEDINGS OF THE 2019 22ND ACM INTERNATIONAL CONFERENCE ON HYBRID SYSTEMS: COMPUTATION AND CONTROL (HSCC '19), 2019, : 77 - 86
  • [42] EQUIVALENCE OF LINEAR TIME-INVARIANT DYNAMICAL SYSTEMS
    ANDERSON, BD
    NEWCOMB, RW
    KALMAN, RE
    YOULA, DC
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1966, 281 (05): : 371 - &
  • [43] Control reconfigurability of linear time-invariant systems
    Wu, NE
    Zhou, KM
    Salomon, G
    AUTOMATICA, 2000, 36 (11) : 1767 - 1771
  • [44] Geometrical design of fractional PDμ controllers for linear time-invariant fractional-order systems with time delay
    Josue Guel-Cortez, Adrian
    Mendez-Barrios, Cesar-Fernando
    Jorge Gonzalez-Galvan, Emilio
    Mejia-Rodriguez, Gilberto
    Felix, Liliana
    PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING, 2019, 233 (07) : 815 - 829
  • [45] ROBUST STABILIZATION OF LINEAR TIME-INVARIANT SYSTEMS
    VERMA, MS
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1989, 34 (08) : 870 - 875
  • [46] The Importance of Continuity for Linear Time-Invariant Systems
    Zhang, Ming
    Chen, Xiaoming
    IEEE SIGNAL PROCESSING MAGAZINE, 2020, 37 (02) : 77 - +
  • [47] Hyperbolicity Radius of Time-Invariant Linear Systems
    Doan, T. S.
    Kalauch, A.
    Siegmund, S.
    DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATI ONS, 2013, 47 : 113 - 125
  • [48] ON TRANSIENT RESPONSES IN LINEAR TIME-INVARIANT SYSTEMS
    IZMAILOV, RN
    DOKLADY AKADEMII NAUK SSSR, 1987, 297 (05): : 1068 - 1071
  • [49] Ensemble Controllability of Time-Invariant Linear Systems
    Qi, Ji
    Li, Jr-Shin
    2013 IEEE 52ND ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2013, : 2709 - 2714
  • [50] CYCLICITY AND CONTROLLABILITY IN LINEAR TIME-INVARIANT SYSTEMS
    ANTSAKLIS, PJ
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1978, 23 (04) : 745 - 746
12345