### General Nonlinear ODE

In state-space form (§1.3.7) [449],^{8.7}a general class of th-order Ordinary Differential Equations (ODE),
can be written as

where denotes time in seconds, denotes a vector of

*state variables*at time ,

In the linear, time-invariant (LTI) case, Eq.(7.8) can be expressed in the usual state-space form for LTI continuous-time systems:

In this case, standard methods for converting a filter from continuous to discrete time may be used, such as the FDA (§7.3.1) and bilinear transform (§7.3.2).

^{8.8}

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