On the observability of conformable linear time-invariant control systems

Abstract

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.

On the solution of the Cayley impulsive dynamic control systems

“…On the other hand, dynamic systems on time scale calculus combine discrete and continuous phenomena [27]. So, hybridization of two different phenomena where the disturbance in the mathematical model concerned and the mixed domain (continuous and discrete ) in the related parameters claims for merging the notions of impulsive dynamic systems and time scale theory [28].…”

Partial Stability of Conformable Stochastic Systems

“…In the last decades, it has established its effectiveness as an essential tool in many real-world applications, such as physics [7], biology [4,8,9], and control theory [2,3,5,[10][11][12][13][14]. In fact, Neirameh in [4] proposed a new method to find exact solutions of the general biological population model.…”

“…Using the fixed-point method, Das in [2] showed the controllability and the existence of mild solution for a class of nonlinear systems. On the other hand, Younus et al in [14] investigated the observability of linear timeinvariant control systems.…”

Stability of conformable stochastic systems depending on a parameter

“…Using the Banach‐fixed point theorem Das in [6] established the controllability for a class of nonlinear systems. Furthermore, Younus et al in [15] studied the observability of linear time‐invariant control systems.…”

“…In particular, the stability theory of the solution of conformable fractional-order nonlinear deterministic and stochastic systems has attracted much more attention (see [6], [7], [8], and [9]). Recently, it has established its effectiveness as an important tools in many fields applications, such as control theory [6,7,[9][10][11][12][13][14][15], physics [16], or biology [8,17,18]. In fact, Neirameh in [8] suggested a method to find exact solitary wave solutions of extended biological population model.…”