Robust Stability and Ellipsoidal Quality Estimates of Interval Multidimensional Control Systems1

The algebraic method of researches of robust stability of continuous and discrete interval dynamical systems is considered, as well as the method of ellipsoidal quality estimates of multidimensional control systems. This paper presents the original results obtained for the research of the stability of continuous and discrete linear interval dynamical systems, called the Algebraic method of robust stability. Ellipsoidal quality estimates based on majorant and minorant estimates calculated using of singular values of corresponding criterion matrices of these properties are proposed for investigation of qualitative properties of multivariate control systems. The computational apparatus for determining ellipsoidal estimates is based on singular value decomposition matrix using standard SVD-procedures. Basic concepts of ellipsoidal estimation method are given.