Global Exponential Observer Research Articles

Continuous-Discrete Observer for State Affine Systems With Sampled and Delayed Measurements

The observation of a class of multi-input multi-output (MIMO) state affine systems with both sampled and delayed output measurements is addressed. These two constraints disturb simultaneously the convergence of the observer. Assuming some persistent excitation conditions to hold, and by using Lyapunov tools adapted to impulsive systems, two classes of global exponential observers are proposed. Some explicit relations between maximum allowable delay and maximum allowable sampling period are given. An extension to some classes of nonlinear systems is also given.

Global exponential observers for two classes of nonlinear systems

This paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems: (i) the class of systems with a globally asymptotically stable compact set, and (ii) the class of systems that evolve on an open set. In the first class, the derived continuous-time observer also leads to the construction of a robust global sampled-data exponential observer, under additional conditions. Two illustrative examples of applications of the general results are presented: one is a system with monotone nonlinearities and the other is a chemostat system.

Continuous–discrete adaptive observers for state affine systems

The observation of a class of multi-input multi-output (MIMO) state affine systems with constant unknown parameters and discrete time output measurements is addressed. Assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses, system observability is ensured and a class of global exponential observers is synthesized.

Global tracking control of a vtol aircraft without velocity measurements

This note develops a nonlinear output-feedback controller to force a nonminimum phase, underactuated vertical take-off and landing aircraft to globally asymptotically track a reference trajectory generated by a reference model. The control development is based on a global exponential observer, some global coordinate transformations, Lyapunov's direct method and an extension of the backstepping technique. Interestingly, the proposed methodology also yields new results for the previously studied problems of stabilization and output tracking or regulation. Numerical simulations illustrate the effectiveness of the proposed controller.

Global observer design for nonlinear systems

This paper is a geometric study of the global observer design for nonlinear systems. Using the theory of foliations, we derive necessary and sufficient conditions for global exponential observers for nonlinear systems under some assumptions. Our proof for these necessary and sufficient conditions for global exponential observers if via defining two equivalence relations known as horizontal and vertical equivalence relations, and constructing two foliations known as horizontal and vertical foliations from these equivalence relations. Finally, as a corollary of our global theorem, we derive necessary and sufficient conditions for local exponential observers of critically Lyapunov stable nonlinear systems.

Dynamic output feedback for observed variable-structure control systems

A global exponential observer is built explicitly for some classes of nonlinear variable structure observed control systems. By using piecewise-continuous output-feedback control laws, or the (continuous) equivalent control for the observer, the unavailable state vector is asymptotically kept on the sliding manifold with exponential decaying error. Some explicit examples are presented.