Admissible and dissipative synchronisation of fractional order singular systems with time delay using event-triggered feedback control

The purpose of this work is to study the admissible and dissipative synchronisation of fractional order singular systems with time delay. The key goal is to use as few network resources as possible while retaining the desired closed-loop performance. An event-triggered control method is used to accomplish this. The Lyapunov function method, linear matrix inequality approach, and mathematical techniques are used to develop new synchronisation criteria that assure the synchronisation error system is Mittag–Leffler stable. Because fractional order differential equations have memory characteristics, which are very different from ordinary differential equations, leading to difficulties in preventing Zeno behaviour related to the event-triggered mechanism of fractional order systems, especially of delayed fractional order singular systems. To solve this issue, we propose a new theoretical framework and a new condition to preclude Zeno behaviours. This derived conditions use inequality techniques and take advantage of a number of fundamental aspects of fractional order calculus. Furthermore, the dissipative synchronous problem of delayed fractional order singular systems is also solved for the first time using the suggested stable criterion in conjunction with some auxiliary characteristics of fractional calculus. Two numerical examples are provided to demonstrate the usefulness of the proposed strategy.