New Designs of Linear Observers and Observer-Based Controllers for Singularly Perturbed Linear Systems.

This paper considers the design of observers for systems with slow and fast modes. The existing methods are able to design independent slow and fast observers with $O(\epsilon)$ accuracy only, where $\epsilon$ is a small positive singular perturbation parameter that indicates separation of system state-space variables into slow and fast. In this paper, the design of independent slow and fast reduced-order observers was performed with very high accuracy $O(\epsilon ^{i}), i=2,3,....$. The results obtained are extended to the design of corresponding observer driven controllers. The design allows complete time-scale separation for both the observer and controller through the decomposition into slow and fast time scales. This method reduces both offline and online computations. The effectiveness of the new methods is demonstrated through both theoretical and simulation results. [ABSTRACT FROM AUTHOR]