The transformation of linear non-stationary observable and controllable systems into stationary systems

• Published in: Journal of applied mathematics and mechanics 1985, Vol.49 (4), p.422-428
• Main Authors: Vavilova, N.B., Kalenova, V.I., Morozov, V.M.
• Format: Article
• Language: English
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/0021-8928(85)90046-2

The methodological problems of the reducibility of some classes of linear non-stationary observable and controllable systems to stationary systems is considered. The constructive use of this property to analyse the controllability and observability of non-stationary systems, and also to solve applied control and estimation problems, is proposed. For practical applications the separation of the classes of non-stationary systems, which can be investigated using simple and effective methods similar to those for analysing stationary systems, is of interest. Linear non-stationary systems for which the fundamental matrix of the solutions can be algorithmically simply constructed using the matrix of the coefficients, pertain to these calsses; in particular systems which can be reduced to stationary systems /1–5/ using the well-known non-degenerate transformation, and also systems which are Lyapunov-reducible /6, 7/. Although for non-stationary systems the sufficient conditions for controllability and observability which do not require a knowledge of the fundamental matrix of the initial system /8–10/ are known, the search for constructive transformations which reduce the initial system to a form suitable for analysing and synthesizing simple control and estimation algorithms is important and useful.