A method of analysis for time-varying parameter systems is investigated in this paper. Applying the theory of sampled data control systems, regarding time-varying parameters as constants in each sampling period, varying the coefficients of a vector differential equation in each sampling period and extending the state space method in control theory, a very useful method of numerical analysis for time-varying parameter systems is obtained.
First, a method of analysis for linear time-varying parameter systems with and without dead time is presented.
Next, it is extended to the case of nonlinear time-varying parameter systems with and without dead time.
By introducing the concept of the variable equivalent gain of a nonlinear element, it is shown that nonlinear systems can be analyzed in the same way as linear systems. A system with dead time can be analyzed similarly as a system without dead time by introducing the time shift operator.
Making use of this method, linear and nonlinear time-varying parameter systems with and without dead time were analyzed by a digital computer to be compared with the results of the analog computer analysis.
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