Discrete-Time State-Space Model

The Discrete-time state-space model uses time-steps to evaluate the discrete approximation of the continuous function. The equations for the discrete-time state-space model are:
$$x_{k+1}=(I+hA)x_k+hBu_k$$
$$y_k=Cx_k+Du_k$$
Where \(h\) is the time constant, \(I\) is the identity matrix, and \(h\) is the timestep. This is typically called a zero-order hold. These can also be re-written as
$$\begin{matrix}
x[n+1]=Ax[n]+Bu[n] \
y[n] = Cx[n]+Du[n]
\end{matrix}$$

[[Observability problem for discrete time systems]]
[[Simulating the T-Handle Dynamics]] – uses the zero-order hold for a discrete time SS model
State-Space Estimators – are typically implemented and analyzed as a discrete model
[[Porter Method]] – uses a version of the discrete state-space model

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