167 Appendix A: MATLAB commands concluded

$\gg$Q=lyap(A,P) [given positive definite $P$ and square $A$, solves $AQ+Q{A}^{\prime }=-P$]

$\gg$ X=lyap(A,B,C) [solves $AX+XB=-C$]

$\gg$ t=-100:0.1:100 [introduces the vector [-100, -100+0.1,$\mathrm{\dots }$ ,100]]

$\gg$ plot(y) [plots the imaginary part of y versus the real part of y]

$\gg$ angle (z) [computes the argument of the complex number z]

$\gg$ laplace((t${}^2$)*exp(2*t)) [computes the Laplace transform of $t^2{e}^{2t}$, and gives values in a variable $s$]

$\gg$ nyquist(T) [plots the Nyquist locus of a given real rational function]

$\gg$ bode(T) [created the Bode pole of a real rational function] Beware: nyquist and bode have difficulties with complex coefficients.

$\gg$ [g,c,d]=gcd(a,b) [computes the greatest common divisor of $a$ and $b$ and expresses the gcd as $ac+bd$]