Discrete optimal guidance for high-order missile and maneuvering target

An explicit closed-form formula of a discrete guidance law for a linear time-invariant, acceleration commanded, arbitrary-order missile and a linear, time-invariant arbitrary-order, maneuvering target is derived. The formula is given in terms of the missile and target transfer functions and responses to initial conditions. Examples are explicitly solved for zero-lag and a first-order missile. As an example, it is shown that the discrete proportional navigation ratio is higher than 3 and time varying in contrast to the continuous case.