observer is applicable. State observers for nonlinear systems High gain, sliding mode and extended observers are the most common observers for nonlinear systems. To illustrate the application of sliding mode observers for nonlinear systems, first consider the no-input non-linear system: where . Also assume that there is a measurable output given by There are several non-approximate approaches for designing an observer. The two observers given below also apply to the case when the system has an input. That is, Linearizable error dynamics One suggestion by Krener and Isidori and Krener and Respondek can be applied in a situation when there exists a linearizing transformation (i.e., a diffeomorphism, like the one used in feedback linearization) such that in new variables the system equations read The Luenberger observer is then designed as . The observer error for the transformed variable satisfies the same equation as in classical linear case. . As shown by Gauthier, Hammouri, and Othman and Hammouri and Kinnaert, if there exists transformation such that the system can be transformed into the form then the observer is designed as , where is a time-varying observer gain. Ciccarella, Dalla Mora, and Germani obtained more advanced and general results, removing the need for a nonlinear transform and proving global asymptotic convergence of the estimated state to the true state using only simple assumptions on regularity. Switched observers: Sliding mode observer As discussed for the linear case above, the peaking phenomenon present in Luenberger observers justifies the use of switched observers. A switched observer encompasses a relay or binary switch that acts upon detecting minute changes in the measured output. Some common types of switched observers include the sliding mode observer, nonlinear extended state observer and uniting observer. The sliding mode observer uses non-linear high-gain feedback to drive estimated states to a hypersurface where there is no difference between the estimated output and the measured output. The non-linear gain used in the observer is typically implemented with a scaled switching function, like the signum (i.e., sgn) of the estimated – measured output error. Hence, due to this high-gain feedback, the vector field of the observer has a crease in it so that observer trajectories slide along a curve where the estimated output matches the measured output exactly. So, if the system is observable from its output, the observer states will all be driven to the actual system states. Additionally, by using the sign