State Transition Matrix

State Transition Matrix

$$ \mathbf{x}_i = \Phi(t_i, t_j)\mathbf{x}_j $$ In the above expression

• \(\Phi(\cdot, \cdot)\) is a state transition matrix,
• \(\mathbf{x}_i\) is a state vector at time \(t_i\),
• \(\mathbf{x}_j\) is a state vector at time \(t_j\),

and note that \(t_i \leq t_j\) or \(t_i \geq t_j\) can be true for a given instance.