h is a row vector and f is a square matrix the effectiveness of an estimator typically depends on a variety factors one of which is the accuracy with which the equations are able to model the physical system because mems actuator 110 can typically be modeled more accurately and consistently than a piezoelectric actuator mems actuator 110 allows for a more easily and accurately modeled system for sampled data systems eqs 3 and 4 become where x k is the discrete time state k kt s t s is the sample period and u k is the input at the time step k the matrix u03c6 relates the propagation of the discrete time state from one time step to the next it is typically computed using the continuous time derivative matrix f and the sample period t s the matrix u03b3 relates the input u at the time step k to the state x at the next time step x k 1 the matrices h and d relating the state x and the input u to the output y typically do not change in going from a continuous to a discrete linear system note that the boldface convention has been dropped in accordance with the notation common in control theory and it is understood that the respective variables are vectors and matrices there are numerous methods of discretization covered by the general discussion above and these may be found in standard texts on control theory such as u201c digital control of dynamic systems u201d by g franklin d powell and m workman or u201c computer controlled systems u201d by k astrom and b wittenmark the following discussion.