Nonlinear Observers for Perspective Time-Varying Linear Systems

Perspective dynamical systems arise in machine vision problems, 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 time-varying linear systems. In particular, assuming a given perspective time-varying linear system to be Lyapunov stable and to satisfy some sort of observability condition, it is shown that the estimation error converges exponentially to zero. Finally, a simple numerical example is presented to illustrate the result obtained. Keyword: nonlinear observer, perspective system, time-varying systems, observability, exponential stability.