CONTRIBUTIONS TO THE STABILITY ANALYSIS OF SYSTEMS USING FUNCTIONAL ANALYSIS METHODS.
SYRACUSE UNIV N Y DEPT OF ELECTRICAL ENGINEERING
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New stability criteria for nonlinear, time-varying control systems both in continuous and discrete form, have been obtained using functional analysis methods. Several of the new results involve simple geometrical constructions in the complex frequency plane which provide the required stability information in a manner similar to the Popov criterion. The contraction mapping fixed point theorem is used to obtain information on the finite time stability of a class of continuous and discrete systems. The discussion on the finite time stability of systems, while not exhaustive in its treatment of different classes of systems, does give a representative indication of what can be accomplished using this fixed point theorem. A class of systems is investigated in which each system consists of a parallel combination of a time-varying gain and a static nonlinear operator, followed by an operator that satisfies an inner product inequality. A second class of systems is investigated in which each system is characterized by a series combination of a time-varying gain and a static nonlinear operator, followed by an operator that satisfies an inner product inequality. A geometrical interpretation, similar to the Popov criterion, is used to determine the stability of a system from these two classes of systems when the operator satisfying the inner product inequality is a linear time-invariant convolution operator. Author
- Operations Research