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IMA Journal of Mathematical Control and Information 1984 1(4):339-358; doi:10.1093/imamci/1.4.339
© 1984 by Institute of Mathematics and its Applications
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Observability of Nonlinear Systems

K. G. MAGNUSSON

Science Institute, University of Iceland Reykjavik

We consider the observability of systems of the form = Ax + Nx, y = Fx, where A is a linear operator and N and F are nonlinear. We show that if the system is linearized about an equilibrium point xe and the linearized system is continuously initially observable, then the nonlinear system is continuously initially observable in some neighbourhood of xe. We then look at conditions under which solutions of the nonlinear system can be extended for all time and consider the problem of stabilizing the system by feedback controls such that the solutions are eventually in the observability neighbourhood of xe. Finally, we apply these ideas to two systems: a wave equation and a diffusion equation with nonlinear perturbations and nonlinear observations.


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