Synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude Kronecker product terms

Synchronization of Complex Dynamical Networks on Time Scales via Pinning Control

“…On the other hand, the theory of time scales, a useful tool to deal with continuous and discrete analysis under a unified framework, was introduced by Hilger in his Ph.D. thesis [31]. With the development of the theory of time scales, the synchronization of complex dynamical networks on time scales has received increasing attention [32][33][34][35][36][37][38][39][40]. For example, in 2016, Liu and Zhang [35] studied the synchronization of linear complex dynamical networks on time scales via pinning impulsive control.…”

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

“…Consider that a controller of the form ( ) = − ( ( ), ); ∀ ∈ R 0+ is used for the continuous-time feedforward transfer function (48) so that ∈ {Φ} and {Φ} is class in Example 13 satisfying an integral type Popov's inequality (21) for all (≥ 0 ) ∈ R + and some finite 0 ∈ R + . That is, the control function belongs to a class satisfying continuoustime integral Popov's inequality.…”

“…The property of asymptotic hyperstability generalizes that of absolute stability [13][14][15] which generalizes the most basic concept of stability of dynamic systems. See, for instance [2,3,11,[13][14][15][16][17][18][19][20][21][22][23][24][25][26], and references therein. It is well known that closed-loop hyperstability is, by nature, a powerful version of closed-loop stability since it refers to the stability of a hyperstable linear feed-forward plant (in the sense of the positive realness of the associated transfer matrix) under a wide class of feedback controllers applied.…”

Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

“…Fortunately, the time scale theory, which was introduced by Hilger [35], can unify the study of continuous and discrete analysis, and the study of dynamic equations on time scales 2 Discrete Dynamics in Nature and Society can contain, link, and extend the classical theory of differential and difference equations [36]. Recently, the theory of time scale calculus has been applied in real-valued neural networks [37][38][39][40][41][42][43] and complex-valued networks [44]. However, to the best of our knowledge, the existence and global stability of anti-periodic solutions of quaternion-valued fuzzy cellular neural networks (QVFCNNs) on time scales have not been considered yet.…”