Discrete-Time Models and Stability of Distributed Parameter Systems

The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of closed loop systems, the transcendental transfer functions have to be approximated in a suitable manner. In this paper, discrete-time model of distributed parameter systems is obtained. The model employs a sample and hold circuit in the loop. The response of the model system is compared with the response obtained by approximating the transcendental transfer function by root factor and other approximations. The stability of linear and nonlinear systems with distributed parameters is investigated by employing the Mikhailov stability criterion.