Note on observer for Lur'e differential inclusion systems

Cluster synchronisation of non‐linearly coupled Lur'e networks with identical and non‐identical nodes and an asymmetrical coupling matrix

“…. , m are assumed to satisfy [20][21][22][23] γ j ≤ḟ j (c j x i (t)) ≤ δ j (2) for all c j x i (t) ∈ R, i = 1, 2, . .…”

“…Common examples of Lur'e systems include the Goodwin model [15], the repressilator [16], the toggle switch [17], the swarm model [18] and Chua¡¯s circuit [19]. Many literatures have focused on the synchronisation of Lur'e systems; see [20][21][22][23]. For example, in [21], Liu et al, were able to globally synchronise a general Lur'e system with complex topology as well as directed and weighted couplings by using a strategy that is based on the absolute stability theory and the Kalman-Yakubovich-Popov (KYP) lemma.…”

“…Guo et al in [22] presented the cluster synchronisation problem of Lur'e dynamical networks, based on the community structure of the networks, they gained sufficient conditions for achieving cluster synchronisation. In [23], Huang et al considered the reduced-order observer of Lur'e differential inclusion systems, and they obtained that if there exists a full-order observer, then there is also a reduced-order observer.…”

Stochastic observer design for Markovian jump Lur'e differential inclusion system

“…More recently, the observer design problem for the Lur'e DI system has become a hot topic [3,4,5,6,7,8,9,10]. Due to different conditions on the set-valued function, the approaches used are also different.…”

“…[4] and [5] designed the observer for the Lur'e DI system via passive approach, i.e., the system matrix confirms to be positive real. Under the same condition as in [5], [6] presented a systematic approach to construct the reducedorder observer for the Lur'e DI system since the reducedorder observer can save more cost than the full-order one. In the sequel works, [7] and [8] discussed adaptive observer and non-fragile observer design problem for the Lur'e DI system, and [10] gave further results on adaptive observer by relaxing sufficient condition.…”