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DynamicSystems

 CharacteristicPolynomial
 compute the characteristic polynomial of a state-space system

 Calling Sequence CharacteristicPolynomial(sys, lambda)

Parameters

 sys - System(ss); a state-space system object lambda - (optional) name

Description

 • The CharacteristicPolynomial command returns the characteristic polynomial, in lambda, of the state-space system sys. The polynomial is the determinant of lambda*I - A, where A is the system matrix of sys and I is the identity Matrix with dimension(A).
 • The optional lambda parameter is used as the indeterminate of the returned polynomial. The default is the value of the DynamicSystems[SystemOptions] discretefreqvar option, if sys is discrete, or the complexfreqvar option, if sys is continuous.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{sys}≔\mathrm{StateSpace}\left(\frac{1}{{s}^{2}+s+1}\right):$
 > $\mathrm{CharacteristicPolynomial}\left(\mathrm{sys}\right)$
 ${{s}}^{{2}}{+}{s}{+}{1}$ (1)
 > $\mathrm{sys}≔\mathrm{StateSpace}\left(\frac{z}{{z}^{2}+az+b},\mathrm{discrete}\right):$
 > $\mathrm{CharacteristicPolynomial}\left(\mathrm{sys}\right)$
 ${{z}}^{{2}}{+}{a}{}{z}{+}{b}$ (2)
 > $\mathrm{CharacteristicPolynomial}\left(\mathrm{sys},w\right)$
 ${{w}}^{{2}}{+}{a}{}{w}{+}{b}$ (3)

 See Also