# American Institute of Mathematical Sciences

• Previous Article
Interpolation of exponential-type functions on a uniform grid by shifts of a basis function
• DCDS-S Home
• This Issue
• Next Article
Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

## On the observability of conformable linear time-invariant control systems

 1 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan 2 Informetrics Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam 3 Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia 4 Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India

* Corresponding author: Devendra Kumar

Received  November 2019 Revised  March 2020 Published  November 2020

In this paper, we analyze the concept of observability in the case of conformable time-invariant linear control systems. Also, we study the Gramian observability matrix of the conformable linear system, its rank criteria, null space, and some other conditions. We also discuss some properties of conformable Laplace transform.

Citation: Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020444
##### References:

show all references

##### References:
 [1] Xu Zhang, Chuang Zheng, Enrique Zuazua. Time discrete wave equations: Boundary observability and control. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 571-604. doi: 10.3934/dcds.2009.23.571 [2] Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $p$ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020442 [3] A. Alessandri, F. Bedouhene, D. Bouhadjra, A. Zemouche, P. Bagnerini. Observer-based control for a class of hybrid linear and nonlinear systems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1213-1231. doi: 10.3934/dcdss.2020376 [4] Yoshitsugu Kabeya. Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3529-3559. doi: 10.3934/dcds.2020040 [5] Lars Grüne, Roberto Guglielmi. On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Mathematical Control & Related Fields, 2021, 11 (1) : 169-188. doi: 10.3934/mcrf.2020032 [6] Peizhao Yu, Guoshan Zhang, Yi Zhang. Decoupling of cubic polynomial matrix systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 13-26. doi: 10.3934/naco.2020012 [7] Yvjing Yang, Yang Liu, Jungang Lou, Zhen Wang. Observability of switched Boolean control networks using algebraic forms. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1519-1533. doi: 10.3934/dcdss.2020373 [8] Max E. Gilmore, Chris Guiver, Hartmut Logemann. Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021001 [9] Yuri Fedorov, Božidar Jovanović. Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020375 [10] Mohamed Aliane, Mohand Bentobache, Nacima Moussouni, Philippe Marthon. Direct method to solve linear-quadratic optimal control problems. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021002 [11] Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020436 [12] Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020046 [13] Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020055 [14] Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026 [15] Duy Phan, Lassi Paunonen. Finite-dimensional controllers for robust regulation of boundary control systems. Mathematical Control & Related Fields, 2021, 11 (1) : 95-117. doi: 10.3934/mcrf.2020029 [16] Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 [17] Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial & Management Optimization, 2021, 17 (1) : 317-337. doi: 10.3934/jimo.2019113 [18] Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discrete-time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 299-336. doi: 10.3934/dcdsb.2020331 [19] Stefan Siegmund, Petr Stehlík. Time scale-induced asynchronous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1011-1029. doi: 10.3934/dcdsb.2020151 [20] Hyung-Chun Lee. Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM. Electronic Research Archive, , () : -. doi: 10.3934/era.2020128

2019 Impact Factor: 1.233