In lecture 1.2, y(x) was used as a function of the state variables. Is y a generic function of vector x?
In control theory, we usually use y to represent the output of a system. This output can be a subset of the state variables x1, x2, x3, etc. depending on the # of states and the states that are accessible for measurement by the sensors. For example, if we have sensor matrix C = [1 0], this could mean that only the first state is accessible by the sensors (or that we don't care about the dynamics of the second state in a 2-D system) and the output will be y = Cx = [1 0]*[x1 x2]' = x1. Thus, in this case the output y is a function of only state x1. You will learn later in the course that an "observer" can be used to estimate states that are not accessible for measurement by the sensors. --Luis Soto 18:56, 1 October 2008 (PDT)