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Represent sparse second-order models in Simulink

**Library:**Control System Toolbox

The Sparse Second Order block lets you to represent second-order sparse
state-space models, in Simulink^{®}. Such sparse models arise from finite element analysis (FEA) and are useful in
fields like structural analysis, fluid flow, heat transfer and electromagnetics. The resultant
matrices from this type of modeling are quite large with a sparse pattern. In continuous time,
a second-order sparse mass-spring-damper state-space model is represented in the following form:

$$\begin{array}{r}\text{M}\ddot{q}(t)+\text{C}\dot{q}(t)+\text{K}q(t)\text{=B}u(t)\\ y(t)\text{=F}q(t)+\text{G}\dot{q}(t)+\text{D}u(t)\end{array}$$

Here, the full state vector is given by $$\left[q,\dot{q}\right]$$, where $$q$$ and $$\dot{q}$$ are the displacement and velocity vectors. `u`

and
`y`

represent the inputs and outputs, respectively. `M`

,
`C`

, and `K`

represent the mass, damping and stiffness
matrices, respectively. `B`

is the input matrix, while `F`

and `G`

are the output matrices resulting from the two components of the
state vector. `D`

is the input-to-output matrix.