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.

$\mathrm{with}\left(\mathrm{DynamicSystems}\right)\:$

$\mathrm{sys}≔\mathrm{StateSpace}\left(\frac{1}{s^2+s+1}\right)\:$

$\mathrm{CharacteristicPolynomial}\left(\mathrm{sys}\right)$

$s^2+s+1$

$\mathrm{sys}≔\mathrm{StateSpace}\left(\frac{z}{z^2+az+b}\,\mathrm{discrete}\right)\:$

$\mathrm{CharacteristicPolynomial}\left(\mathrm{sys}\right)$

$z^2+az+b$

$\mathrm{CharacteristicPolynomial}\left(\mathrm{sys}\,w\right)$

$w^2+aw+b$