Computer realization of stability criteria for linear systems of differential equations (Q2901680)

There are considered linear differential equations with constant coefficients of the following types: NEWLINE\[NEWLINE \frac {dx(t)}{dt} = A x(t), NEWLINE\]NEWLINE with the corresponding constant-delay equations NEWLINE\[NEWLINE y^{(n)} (t) + \sum\limits_{k=1}^{n} \left[ a_{n-k} y^{(n-k)}(t) + \sum\limits_{j=1}^{m_k} b_{n-k,j} y^{(n-k)}(t-\tau_{n-k,j}) \right] = 0, NEWLINE\]NEWLINE and with periodic coefficients NEWLINE\[NEWLINE \frac {dx(t)}{dt} = A(t) x(t), NEWLINE\]NEWLINE where \(A(t+T)=A(t)\). For each type of the system, the possibility of using classical stability criteria, such as Routh's criterion and Mikhailov's criterion, is studied. Besides that, the authors describe the main difficulties arising at the implementing the algorithm of stability checking by these criteria in mathematical package Maple. Authors describe the ways allowing to overcome the above difficulties, also. In particular, the finitization method is proposed for the Mikhailov criterion. All described results are accompanied by numerical calculations for some model examples.