Dear editor,rnMany real-world systems exhibit a two-time-scale behavior,such as Hindmarsh-Rose oscillators,DC motors,power net-works,and other related systems.Such systems can be mod-eled using singularly perturbed systems(SPSs).To alleviate the difficulties of high dimensionality and stiffness,Koko-tovi? et al.[1]developed the singular perturbation method for reducing the model order,whereby the full system de-sign is divided into designing separate controllers for fast and slow subsystems.In this regard,O'Reilly[2]proposed a composite full-order observer design method for linear SPSs through observer design in two separate time-scales.Later,the two-time-scale observer design was extended to nonlin-ear systems[3,4].However,in many engineering systems with two-time scales,the slow subsystems usually represent the“dominant”parts of the plants,while the fast subsys-tems represent the“parasitic”parts.