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→Linear systems solutions: expanding on the explanation of zero-input and zero-state responses |
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: <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 first term is known as the '''zero-input response''' and represents how the system's state would evolve in the absence of any input. The the second term is known as the '''zero-state response''' and defines how the inputs impact the system.
==Peano–Baker series==
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