Linear state space equations

Linear state space equations consist of a (difierential) state equation?

x = Ax + Bu

and an (algebraic) output equation

y = Cx + Du

where u is the input, x is the state, y is the output. The matrices are called by various names. Typicallywe say A is the plant matrix, B is the input matrix, C is the output matrix,D is the transmission matrix.T

he above format covers all systems which have transfer functions and transfer function matrices where the order 1 of the numerator is less than or equal to that of the denominator. Transfer functionsfor real physical systems must have this property.Sometimes what appears to be a slightly difierent structure for the state space equations is used to separate out special inputs such as disturbances or control commands, or to separate out special outputs such as transducer measured outputs or controlled outputs. These apparantly difierent forms are actuallystill special cases of the above model.