Matrix difference equation

A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, is an example of a second-order matrix difference equation, in which x is an n × 1 vector of variables and A and B are n × n matrices. This equation is homogeneous because there is no vector constant term added to the end of the equation. The same equation might also be written as