変分表現を用いた線形制御系の時変的係数変動の影響の研究

概要

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Parameters of the linear system in operation usually deviate from its nominal values used for the design. These deviations are generally time-varying and yield nonlinear effects even if the system is linear. Thus, it is difficult to deal with the time-varying parameter variations in the framework of linear system theory. In this paper, we give a variational expression for the output variation Δy (t) caused by the variable parameter term δμi (t) Dix (t) in the linear system. Using the expression, we can derive a necessary and/or sufficient condition for its first variation δy (t) to vanish in the open loop system, which are extended to the closed loop system with state feedback and reference input. This variational expression and derived conditions are useful for sensitivity analysis of structured parameter variations in linear systems.