Observable vector feedback digital controller

A method for designing a partial state feedback controller for single-input single-output linear discrete systems is presented. It is based on minimizing a quadratic cost function with respect to the feedback parameters. Because a global optimal control does not exist for partial state feedback controls, that is, the minimum cost control is a function of the initial condition, the cost function is minimized for a particular initial condition. It is shown that the resulting partial state feedback control always stabilizes the closed-loop system. As in the full state optimal control, the desired control us determined by choosing an appropriate cost function