Perhaps all natural and physical systems are governed by non-linear laws of nature. The dynamics of most of such systems can be mathematically represented by non-linear di!erential or integral equations, which can be studied by analytical or numerical techniques. These techniques, in many instances, can successfully explain certain phenomena that are exclusive to non-linear systems. One such phenomenon is the limit cycle (periodic) behavior of systems. Limit cycles can be considered as both desirable and unwanted responses of systems. For instance, oscillators (see, e.g., reference [1]) or certain types of lasers, such as self-pulsatig lasers (see, e.g., reference [2]), are expected to exhibit limit cycle behavior. However, in a positioning system, limit cycles are certainly unwanted and should be suppressed (see, e.g., reference [3]). In the past decades, researchers have devised techniques to suppress limit cycles in non-linear systems: see, e.g., references [4}11] and the references therein.
In this note, it is shown that an e!ective means of suppressing e!ects of non-linearities, and consequently possible limit cycles in a class of non-linear systems, is the application of disturbance observers. Disturbance observers are useful tools that were originally proposed in references [12,13] as means of estimating disturbances to linear systems and cancelling them subsequently. Later, the theory of disturbance observers was advanced in reference [14]. Presently, disturbance observers are successfully used in achieving robust stability and performance in motion control systems, for instance, robotic systems, high-speed machining systems, (micro) positioning systems, disk drives; see e.g., references [15}21] and the references therein. It appears that disturbance observers are mostly designed for linear systems. There are some works where the application of disturbance observers to non-linear systems is reported; see references [11, 22}27]. The present note illustrates that disturbance observers can make members of a certain class of non-linear systems behave linearly.
The organization of the note is as follows. In section 2, the class of non-linear systems to be studied is presented. A non-linear system in this class has the property that its output is equal to the summation of the output of a stable single-input}single-output (SISO) linear