Frequency Domain Input–Output Analysis of Sliding-Mode Observers

The sliding-mode (SM) observer dynamics are analyzed in the frequency domain. It is shown that the SM observer is essentially a relay feedback-feedforward system. It is feedback with respect to the measured variable of the system being observed, and the feedforward with respect to the control applied to the system being observed. Having noted this, the input-output properties of observer dynamics are analyzed with the use of the locus of a perturbed relay system (LPRS) method. The performance of the observer is assessed via the use of the frequency response techniques. An example of performance analysis of the observer dynamics in the frequency domain is given