State Space Models

*Equations of motion* for any physical system
may be conveniently
formulated in terms of the *state* of the system [333]:

Here, denotes the

Equation (1.6) is diagrammed in Fig.1.4.

The key property of the state vector
in this formulation is
that it *completely determines the system at time
*, so that
future states depend only on the current state and on any inputs at
time
and beyond.^{2.8} In particular, all past states and the
entire input history are ``summarized'' by the current state
.
Thus,
must include all ``memory'' of the system.

- Forming Outputs
- State-Space Model of a Force-Driven Mass
- Numerical Integration of General State-Space Models
- State Definition

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University