Modal Representation

When the state transition matrix
is *diagonal*, we have the
so-called *modal representation*. In the single-input,
single-output (SISO) case, the general diagonal system looks like

Since the state transition matrix is diagonal, the modes are

Thus, the diagonalized state-space system consists of
*parallel one-pole systems*. See §9.2.2
and §6.8.7 regarding the conversion of direct-form filter
transfer functions to parallel (complex) one-pole form.

- Diagonalizing a State-Space Model
- Finding the Eigenvalues of A in Practice
- Example of State-Space Diagonalization
- Properties of the Modal Representation

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