Control schemes that achieve stabilization and output regulation in the case of non-minimum phase nonlinear systems are presented. These techniques utilize continuously implemented sliding mode control, and an extended high-gain observer to generate estimates of the output and its first ρ - 1 derivatives (ρ is the relative degree of the system), in addition to a signal that renders the zero dynamics of the given plant observable. The results include exponential stability of the origin of the output feedback system in the stabilization problem, exponential stability of the origin of the error system in the regulation problem, and asymptotic recovery of the performance of the state feedback designs in both instances.The stabilization and regulation problems pose unique challenges in the case of non-minimum phase nonlinear systems. This work provides a design methodology that can be incorporated into any robust control scheme. The design process conforms to the nonlinear separation principle, and comprises the following three steps.1) Augment a dynamic stabilizing compensator to the system and moreover, design it such that the resultant system is minimum phase and relative degree one with respect to a virtual output to be constructed using the state estimates.2) Use any robust control technique such as sliding mode control, saturated high-gain feedback, Lyapunov redesign, etc. to design a static state feedback control law that stabilizes the relative degree one minimum phase system obtained in the previous step.3) Design an extended high-gain observer (EHGO) to estimate the system output and its first ρ - 1 derivatives, and additionally, the coupling signal that is required to solve the auxiliary design problem stemming from step 1). Replace all the states and the coupling signal in the state feedback control design with their estimates, and if necessary, saturate the resulting control law outside a compact set of interest, or saturate the estimates obtained from the EHGO.Simulation examples are provided — in particular, the stabilization algorithm is applied to the Translational Oscillator with a Rotating Actuator (TORA) nonlinear benchmark system.
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