On Uniformity Of Some Control Properties For Linear Singularly Perturbed Systems

In this dissertation, the uniformity issue of small parameter on linear time-invariant parameterized normal system is addressed where the controllability, observability, stabilizability and detectability are studied.A new field of viewing a singularly perturbed system as a parameterized normal system is considered, when the interval of the parameter is within a bound but not closed interval. The dependence of the system on ε is discussed for this parameter-ized normal system where by the system orders are reduced as ε â†' O.The controllability, observability, stabilizability and detectability of this param-eterized normal system for a class of time-invariant linear systems are discussed as they play important role in designing controllers. Here the rank criterion is used to show the controllability and observability while linear matrix inequality method is used to show stabilizability and detectability of the two time scale control system. Sufficient conditions for parameterized normal system to be uniformly controllable, uniformly observable, uniformly stabilizable and uniformly detectable have been ob-tained.