Using a high-gain observer for a hybrid output feedback: Finite-time and asymptotic cases for SISO affine systems

Abstract

This article suggests a design method of hybrid output feedbacks for affine systems under observability and stabilizability assumptions. Our aim is to use the separation principle on systems controlled by hybrid feedback laws. We investigate two constructive methods for the high-gain observer: the first one is based on a finite-time convergence of the observation error, the second one is based on an asymptotic convergence of the observation error. We illustrate one of our main results on a well-known example: integrators chain.

Semi-global stabilization by an output feedback law from a hybrid state controller

“…Consequently, despite the fact that the dynamics are linear, the stabilization problem for this system is not an easy task although recent works Yuan and Wu (2015); Hu et al (2006) propose design methods for saturated actuator. The strategy presented in this paper can be also efficient for purely nonlinear systems as it is shown in Marx et al (2014) where it is proven the existence of a hybrid output feedback for a chain of integrators with a nonlinearity from a state feedback uniting a global and a local controllers. Following Loquen et al (2007), we compute the hybrid controller such that A = {0} × {0} × {0} × [0, 1] is locally asymptotically stable for the FORE system…”

“…Remark 2. In Marx et al (2014), from a weaker observability assumption, i.e. an observability property holding for just one control, a finite-time convergent observer and a hybrid state feedback controller has been used to design an output feedback law.…”

“…Note that this paper is an extension of the conference paper Marx et al (2014). It includes a missing part (the observer design), proofs and a new illustration.…”