ある分布定数系の安定性

抄録

Stability of distributed parameter systems is analyzed by using a Lyapunov function of the quadratic form of the state variables. The system considered is described by the second order partial differential equation with constant coefficients and multiple nonlinear functions.
A sufficient condition for the asymptotic stability of the steady states is represented in terms of the conditions related to given boundary conditions, and of the positive definite condition of a certain matrix in the frequency domain. The latter condition may be considered as an extension of the circle criterion for lumped parameter systems to distributed parameter systems.
As an example, a problem in chemical reactions with mass and heat diffusion is treated. It is shown that the stability of such a system can be determined mainly by the steady state values and the characteristics of nonlinear functions. Two numerical analyses are also given.