Quantized state systems method: Difference between revisions

Revision as of 09:54, 6 July 2015

Revision as of 09:56, 6 July 2015

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The pattern continues for higher-order approximations, which define the quantized state <math>q(t)</math> as successively higher-order polynomial approximations of the system's state.

It is important to note that, while in principle a QSS method of arbitrary order can be used to model a continuous-time system, it is seldom desirable to use methods of order higher than four, as the [[Abel–Ruffini theorem]] implies that the time of the next quantization, <math>t</math>, cannot (in general) be [[Explicit and implicit methods|explicitly solved]] for [[algebraic solution|algebraically]] when the polynomial approximation is of degree greater than four, and hence must be approximated iteratively using a [[root-finding algorithm]]. In practice, QSS2 or QSS3 can proveproves sufficient for many problems and the use of higher-order methods results in little, if any, additional benefit.

==Backward QSS method – BQSS==