GREATEST VALUES OF MAIN PARAMETERS AND A CRITERION FOR THE BOUNDEDNESS OF THE CHARACTERISTIC DOMAIN OF ASYMPTOTIC STABILITY OF LINEAR-SYSTEMS

For the multidimensional stability domain in the space of coefficients of the characteristic polynomial, the existence of a ''vertex'' is proved, its coordinates are found analytically, a bounding parallelepiped with unimprovable characteristics is constructed, and the maximal value of the boundary frequency is found. Necessary conditions for the stability of an arbitrary family of characteristic polynomials are suggested.