Stability of a class of linear switching systems with time delay

Abstract

We consider a switching system composed of a finite number of linear delay differential equations (DDE). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODE) may be achieved by using a Common Lyapunov Function Method switching rule. We modify this switching rule for ODE systems to a Common Lyapunov Functional Method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati type Lyapunov functional under a condition on the time delay.

Leader–follower guaranteed-cost consensualization for high-order linear swarm systems with switching topologies

“…The LMI tools were extensively used to deal with stabilization problems of isolated switching systems (e.g., [50,51]) and can also be applied to study consensus analysis and design problems of swarm systems with switching interaction topologies (e.g., [52,53]). However, it should be pointed out that if the dimensions of all variables of LMI consensus conditions are dependent on the number of agents, then the scalability of swarm systems cannot be guaranteed; that is, the calculation complexity of those conditions increases significantly when the number of agents increases.…”

Almost output regulation for turbofan switched systems under multi‐source disturbances and time delay

“…Moreover, time delay often occurs in the practical engineering applications, especially in the turbofan control systems. Due to the changes of dynamic and the effect of time delay, the characteristics of switched delay systems is usually more complex than those of pure switched systems or time delay systems 35‐37 . Thus, it is more meaningful to investigate the turbofan switched systems subject to time delay.…”

A multi-thread control algorithm with update delays based on event-triggered mechanism

“…It was first introduced into control theory in the 1960s and has been widely used in traffic control, intelligent robots, and several other fields. [5][6][7] Switching rules play a crucial role in switching systems. Different switching rules cause different action sequences for the subsystems, resulting in different dynamic characteristics of the system.…”

“…It was first introduced into control theory in the 1960s and has been widely used in traffic control, intelligent robots, and several other fields. 5–7…”