Luenberger-type observers for perspective linear systems

Perspective dynamical systems arise in machine vision, in which only perspective observation is available, and the essential problem is to estimate the state and /or unknown parameters for a moving rigid body based on the observed information. This paper proposes and studies a Luenberger-type observer for perspective linear systems. In particular, assuming a given perspective linear system to be Lyapunov stable and to satisfy some sort of detectability condition, it is shown that the estimation error converges exponentially to zero. Finally, some simple numerical examples are presented to illustrate the result obtained.