This paper presents a formula for determining the initial condition of a controller expressed in a descriptor form to avoid the following unexpected results. It is pointed out that the initial condition of a derivative controller should be chosen taking into account that of the plant under control, to avoid plant responses that are vastly different from intended ones, even if the controller is designed properly otherwise. Although the initial condition is often set simply to zero without realizing such possibilities, simulations show that the response of a nonlinear system can diverge even from an initial state close to its stable equilibrium.
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