Fault detection for discrete spatially interconnected systems with time-delay over finite frequency domains

Exponential stability analysis and model reduction for spatially interconnected discrete‐time systems with time‐varying delay

“…In particular, the time delay under consideration is time‐varying, which is a more realistic condition, rather than constant time‐delay. Secondly, we derive a sufficient delay‐dependent condition in the form of LMI for checking the well‐posedness, exponential stability and contractiveness of the given systems. This result can also be applied to spatially interconnected discrete‐time systems subject to constant time‐delay, that is to say, this result is a generalisation of the result in [11]. Thirdly, based on the stability and performance analysis result for spatially interconnected discrete‐time systems with time‐varying delay, a sufficient condition for guaranteeing the existence of a structure‐preserving reduced‐order system is derived.…”

“…Moreover, letting , i.e. time‐delay in spatially interconnected discrete‐time delay system is constant, we can see that the well‐posedness and exponential stability analysis for the systems in Theorem 1 reduces to Theorem 3.2 in [11]. Therefore, Theorem 1 can be seen as a generalisation of the corresponding outcome on stability analysis for a spatially interconnected discrete‐time system subject to constant time‐delay in [11].…”

“…Meanwhile, the distributed control design has also studied in [4, 5]. Afterwards, considerable research studies on the spatially interconnected system have been carried out, such as the stability and performance analysis [6, 7], model reduction [8], the frequency domain properties analysis [9–11], and so forth.…”

“…It is worth mentioning that the time‐delays appear in the signal transmission process between the subsystems. When considering time‐delay occurs in system state, the authors in [11] studied the asymptotical stability of spatially interconnected discrete‐time systems subject to constant time‐delay. However, in engineering applications, the time‐varying delay is more common than the constant delay.…”