2 дек. 2017 г. · Here equation (3.12) is PA+ATP=−Q. How is the 3×3 matrix on the left-side of the first matrix equation formed?

21 февр. 2018 г. · Is there a direct way to solve the simplified Lyapunov equation for P without implicitly or explicitly using the knowledge of the final solution ...

12 апр. 2017 г. · So this might only be solvable when n=1 (and n=0). For larger n there are infinitely many solutions, or you would have to add additional ...

10 мар. 2015 г. · Suppose that A is constant. Let us take P(t)=exp(−tAT)R(t)exp(−tA),. where R(t) is some matrix. We can write the derivative of P: ...

5 мая 2015 г. · The existence of P=P∗>0 satisfying the Lyapunov equation is a sufficient criterion. We have explicit formulas for solutions of the Lyapunov ...

24 янв. 2013 г. · X = lyap(A',Q) solves the continuous-time Lyapunov equation ATP + PA + Q = 0 so, you can solve the lyapunov function.

10 сент. 2021 г. · As is noted on the Wikipedia page about the Lyapnov equation, the (unique) solution to this equation can be written as X=∫∞0eATτQeAτdτ.

15 июл. 2020 г. · Given Lyapunov equation: AP+PAT+Q=0 and the linear system ˙x=Ax is globally asymptotically stable i.e. the real part of all eignvalues of A is ...

12 мая 2014 г. · The equation AX−XA=B is equivalent to (I⊗A−AT⊗I)vec(X)=vec(B) (the difference of Kronecker products is not A⊗IT−I⊗AT).

15 мая 2020 г. · I have a linear dynamical system: dxdt=Ax with A∈Rn×n and x∈Rn×1. I consider a quadratic function V(x)=xT ...