Robustness to Regular and Singular Perturbations
The objective of this chapter is to present a framework wherein robustness properties of H∞ controllers obtained in Chapters 4 and 5 can be studied in the presence of small perturbations on the original system dynamics — such as small nonlinearities (for linear systems), unmodeled fast dynamics, and unmodeled weak coupling between subsystems of a large-scale system. This general framework will first be introduced in a context where the controller has access to perfect-state measurements (as in Chapter 4), and then extended to the imperfect-state measurements case only for linear systems. This will allow us to state precise robustness results for H∞ controllers.
KeywordsSingular Perturbation Fast Dynamic Disturbance Attenuation Fast Subsystem Attenuation Level
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