TABLE OF CONTENTS The state model of a linear, time-invariant MIMO system is a special case of the general time-invariant state model of Equations (1.6). In state representation, the derivative of each state variable can be written as a linear combination of system states and inputs i.e.,
where coefficients a ij; i = 1, 2, , n; j = 1, 2, n and b ik; i = l, 2, ,. n; k = 1, 2, , m are constants. Equations (1.8) may be written in vector-matrix form as
Similarly, the output variables can be written as a linear combination of system states and inputs, i.e.,
where, coefficients c ij; i = 1, 2, p; j = 1, 2, n and d ik; i = 1, 2, p: k = 1, 2, m are constants. Equations (1.9) may be written in vector-matrix form as
The state equation and output equation together constitute the state model of the system. Thus, the state model of a linear time-invariant MIMO system is given as
The state model of a linear, time-varying MIMO system is of the same form as given in Equations (1.10) except for the fact that the coefficients of the matrices A, B, C, and D are no longer constants but are the functions of time.
Thus, the state model...
