Semi-Global Output Feedback Stabilization of Non-Minimum Phase Nonlinear Systems

Abstract

We solve the problem of output feedback stabilization of a class of nonlinear systems, which may have unstable zero dynamics. We allow for any globally stabilizing full state feedback control scheme to be used as long as it satisfies a particular ISS condition. We show semi-global stability of the origin of the closed-loop system and also the recovery of the performance of an auxiliary system using a full-order observer. This observer is based on the use of an extended high-gain observer to provide estimates of the output and its derivatives plus a signal used by an extended Kalman filter to provide estimates of the remaining states. Finally, we provide a simulation example that illustrates the design procedure. stabilization was achieved under similar assumptions but with an extended-high-gain-observer-based output feedback controller.

A filtered high gain observer for a class of non uniformly observable systems – Application to a phytoplanktonic growth model

“…Notice that the dynamics of the Riccati equation (13) involved in Assumption A4 depends on the state estimate x as in [18,19] and not on the state x. At a first glance, it would seem more natural to express Assumption A4 using the state rather than its estimate.…”

“…On other aspects, Assumption A4, which is similar to that considered in [18,19], is of a primary importance for the stability of the observer. Indeed, as noted in [18], this assumption is satisfied for uniformly observable systems, i.e.…”

Adaptive Backstepping Sliding Mode Control for Boost Converter With Constant Power Load

“…Additionally, this method cannot be directly applied to systems with unstable zero dynamics [11]. Therefore, when the system does not meet the conditions of exact linearization, it is also necessary to consider the stability of zero dynamics; otherwise, the system may be non-minimum phase, resulting in negative regulation characteristics [12]. This deteriorates the dynamic quality of the control system, resulting in a prolonged system transition time.…”

Global exponential stabilization for a class of nonlinear systems by output feedback control with three gain‐scaling factors

“…Output feedback control problems have received much attention in the control field and several related results for nonlinear systems have been reported, for example, References 1‐20. In these regards, most reported results on the output feedback control for a class of nonlinear systems have certain conditions on the perturbed nonlinearities such as lower triangular conditions, 1‐3,21 upper triangular (feedforward) conditions, 4‐6,21 and nontriangular conditions 1,3,7 .…”