The problem of the measure of robust stability, modality, and aperiodicily of continuous, discrete, and distributed linear systems with linear parameters is solved. The nonlinear and matrix cases are analyzed.The problem of robust stability has its origins in the well-known work of Kharitonov [1]. Recently, this problem has received considerable attention, as is evidenced by the large number of publications in Russia and elsewhere, the new surveys (e.g., [2][3][4] and others), and special topical symposia and conferences. This attention to the problem is a consequence of its general theoretical significance and considerable applied value.The general theoretical significance of the problem stems from the fact that it constitutes a development of stability theory and is closely related to bifurcation theory and the problem of robustness of dynamical system. Robust stability was considered in implicit form, as an algebraic problem, back in the 19 th century in the work of P. L. Chebyshev and A. A. Markov [5]. The classical theoretical results on absolute stability fall in the same category. The applied value of robust stability is attributable to the fact that robust stability is a necessary condition of reliable operation of technical systems, a guarantee of universality of the control system.In its general form, the robust stability problem involves determining the constraints on the system parameters when the system remains stable. These constraints obviously define the stability region with respect to the corresponding parameters. However, the stability region in its direct form can be efficiently used only if it is geometrically visible, i.e., in the twoand three-dimensional cases. With a large number of parameters, this path is closed, but we can instead specify multidimensional regions of a simple form, such as right parallelepipeds, ellipsoids, simplexes, or polytopes, that are entirely included in the stability region.An impetus for the emergence of the robust stability problem was provided by the previously mentioned work of Kharitonov [1], in which he showed that all polynomials of the family ao+alz+...+a,z", la,-a;l
