Stability and performance analysis of a certain class of nonlinear time varying feedback control systems

Abstract

The partitioning technique and the state variable approach have been applied to analyze and to study the behaviour of a control system whose dynamic performance can in general be described by a nonlinear differential equation containing some linear, some nonlinear, and a forcing function terms. 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 L2 space. Under the assumed restrictions, the admissible system was found to satisfy the definition of asymptotic stability in the sense of Lyapunov. Utilizing 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 system remain. Included will be found an example to illustrate the method presented.