1.8 HOMOGENEOUS AND NONHOMOGENEOUS LINEAR TIME-INVARIANT SYSTEMS

The state equation of a linear time-invariant system is given by

Case 1. If A is a constant matrix and u (t) is a zero vector, i.e., no control forces are applied to the system, then the Equation (1.18) represents a homogeneous linear time-invariant system.

Case 2. If A is a constant matrix and u (t) is nonzero vector, i.e., control forces are applied to the system, then Equation (1.18) represents a nonhomogeneous linear time-invariant system.