Content deleted Content added
Fixed 3rd equation by adding x(t_0) to the first term |
|||
Line 6:
: <math>\mathbf{y}(t) = \mathbf{C}(t) \mathbf{x}(t) + \mathbf{D}(t) \mathbf{u}(t)</math>
The general solution is given by
: <math>\mathbf{x}(t)= \mathbf{\Phi} (t, t_0)\mathbf{x}(t_0)+\int_{t_0}^t \mathbf{\Phi}(t, \tau)\mathbf{B}(\tau)\mathbf{u}(\tau)d\tau</math>
The state-transition matrix <math>\mathbf{\Phi}(t, \tau)</math>, given by
: <math>\mathbf{\Phi}(t, \tau)\equiv\mathbf{U}(t)\mathbf{U}^{-1}(\tau)</math>
| |||