Stabilization of Linear Systems with Two Time Scales
In many situations the mathematical models used to describe the object to be regulated exhibit in a natural way several time scales. To illustrate this idea we shall consider only two examples. In the mathematical modeling of a synchronous machine, the evolution of the mechanical part is much slower than the one corresponding to the electrical one.
KeywordsImplicit Function Theorem Feedback Gain Optimal Cost Linear Control System Synchronous Machine
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Notes and References
- There are several sources for general aspects concerning singularly perturbed systems ,  and their references. Separation of time scales can be found in , but was used much earlier in . A general survey concerning the use of singular perturbations in control is , where an extended list of references is given. A previous survey is also [41). An extended list of references is given in . The book  contains a nice chapter on singular perturbations, where the time interval is also [0, ∞). The results in Section 3.3 and Section 3.4 are based on  and , respectively.Google Scholar