# Quantized state systems method

The quantized state systems (QSS) methods [CK06] are a family of numerical integration solvers based on the idea of state quantization.

## First-order QSS method – QSS1

Let an initial value problem be specified as follows.

${\displaystyle {\dot {x}}=f(t,x),\quad x(t_{0})=x_{0}.}$

QSS1 approximates the above system by

${\displaystyle {\dot {x}}=f(t,q)}$

where ${\displaystyle x}$ and ${\displaystyle q}$ are related by histeretic quantization functions.

## Software implementation

The QSS Methods can be implemented as a discrete event system and simulated in any DEVS simulator.

QSS methods constitute the main numerical solver for PowerDEVS[BK011] software. They have also been implemented in as a stand alone version

## References

• [CK06] {{#invoke:citation/CS1|citation

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