State Space Filters

An important representation for discrete-time linear systems is the
*state-space* formulation

where is the length

The state-space representation is especially powerful for
*multi-input, multi-output* (MIMO) linear systems, and also for
*time-varying* linear systems (in which case any or all of the matrices
in Eq.
(G.1) may have time subscripts
) [37].
State-space models are also used extensively in the field of
*control systems* [28].

An example of a Single-Input, Single-Ouput (SISO) state-space model appears in §F.6.

- Markov Parameters
- Response from Initial Conditions
- Complete Response
- Transfer Function of a State Space Filter

- Transposition of a State Space Filter
- Poles of a State Space Filter
- Difference Equations to State Space
- Converting to State-Space Form by Hand
- Signal Flow Graph to State Space Filter
- Controllability and Observability
- A Short-Cut to Controller Canonical Form
- Matlab Direct-Form to State-Space Conversion
- State Space Simulation in Matlab
- Other Relevant Matlab Functions
- Matlab State-Space Filter Conversion Example

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

- Repeated Poles

- Digital Waveguide Oscillator Example

- References
- State Space Problems

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