STABILITY AND PERFORMANCE ANALYSIS OF A CERTAIN CLASS OF NONLINEAR TIME-VARYING FEEDBACK CONTROL SYSTEMS.
MICHIGAN UNIV ANN ARBOR INST OF SCIENCE AND TECHNOLOGY
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The partitioning technique and the state variable approach were applied to analyze and to study the behavior of a control system whose dynamic performance can in general be de scribed by a nonlinear differential equation containing some linear terms, some nonlinear ones, and a forcing function. By placing suitable restrictions on the system equation, it was found that the state variables, which represent the state of the system, belong to an L sub 2 space. Under the assumed restrictions, the admissible system was found to satisfy the definition of asymptotic stability in the sense of Lyapunov. By use of two different definitions of the norm, the system trajectory was analyzed. During the interval of operation considered, expressions for the required norms were obtained inside which all possible states of the system remain. An example is given to illustrate the method. Author