LAUSR

Dear editor, Many real-world systems exhibit a two-time-scale behavior, such as Hindmarsh-Rose oscillators, DC motors, power networks, and other related systems. Such systems can be modeled using singularly perturbed systems (SPSs). To alleviate the difficulties of high dimensionality and stiffness, Kokotović et al. [1] developed the singular perturbation method for reducing the model order, whereby the full system design 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 nonlinear 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 subsystems represent the “parasitic” parts. For example, in an instrumented system, the slow and fast subsystems represent the process dynamics and the sensor dynamics, respectively, while the perturbation parameter represents a measure of the relative speed/time constant of the sensor dynamics. For these systems, fast subsystems are typically considered as unmodeled dynamics, and could be neglected if they are asymptotically stable. Consequently, questions related to robustness arise in relation to the design of control and estimation algorithms based on the approximate slow dynamics. In [5–7], slow reduced-order observers for linear and nonlinear SPSs were designed, and the observation errors generated by neglecting the unmodeled fast dynamics were obtained. Recently, feedback control based on slow dynamics was studied in [8, 9]. We note that the reduced-order observer designs considered in [5–7] are based on the assumption that the output measurements are continuously available. However, in the context of digital control, the measurements are generally available at discrete instants of time due to the use of digital sensors. Therefore, it is important to expand the observer design approach as mentioned above to the discrete time measurement case. This research studies the observer design problem for a class of SPSs with sampled measurements. Our objective is to design continuous-discrete time observers of slow states based only on an approximate model of the slow dynamics. To the best of the authors’ knowledge, this is the first attempt to develop a slow state estimation algorithm for SPSs via sampled measurements. The main contribution of this research is with regard to two aspects. First, a method is proposed for using a single continuous-discrete time observer for slow state estimation in a singularly perturbed system with discrete measurements. Second, the estimation on the observation error is obtained by applying the singularly perturbed theory and the time-dependent Lyapunov functional method, which characterizes the effects of the singular perturbation parameter and the sampling period on the observation accuracy. In