Local observer design for periodic orbits

In this paper, we define the observer design problem for periodic orbits of nonlinear systems and solve the exponential observer design problem by geometric methods. First, we obtain necessary and sufficient conditions for local exponential observers for periodic orbits that are Lyapunov stable. We also show that the definition of local exponential observers can be considerably weakened for periodic orbits that are neutrally stable. As an application of our local observer design of periodic orbits, we consider a class of periodic orbits of nonlinear systems with an input generator (exosystem) and show that for this class of periodic orbits, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs.