an:02170197
Zbl 1065.93030
Antonovskaya, O. G.
On the maximum possible negativity margin for the first derivative (first difference) of a quadratic Lyapunov function
EN
Differ. Equ. 39, No. 11, 1645-1647 (2003); translation from Differ. Uravn. 39, No. 11, 1562-1563 (2003).
00105181
2003
j
93D30 93D05 15A06 15A18 34D08
linear system; quadratic Lyapunov function; negativity margin; level surface; eigenvalues
Consider the linear system
\[
\dot{x} = Ax
\]
and the quadratic Lyapunov function
\[
V(x) = x^TPx
\]
such that \(A\) is Hurwitz and \(P>0\). If the derivative of \(V\) along the system, i.e. \(W(x) = x^T(A^TP + PA)x\), is considered, it is stated that its maximal value on the level surface \(V(x) = V_0\) is not less than \(2(\max_i\{\Re\,\lambda_i\})V_0\) where \(\lambda_i\) are the eigenvalues of \(A\). A discrete-time analogue is also stated.
Vladimir R??svan (Compi??gne)