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On some specific features of linear discrete descriptive systems
Dragutin Lj. Debeljkoviæ Miæa B. Jovanoviæ Stevan A. Milinkoviæ Vesna Drakuliæ
Discrete descriptive systems are those the dynamics of which is governed by a mixture of algebraic and differential equations. In that sense, the algebraic equations represent the constraints which must be fulfilled in every moment of the system behavior. It means that a general solution of system equations has to possess the same properties. The complex nature of discrete descriptive systems causes many difficulties in the analytical and numerical treatment of such systems, particularly when there is a need for their control. In that sense the question of their stability deserves great attention and is tightly connected with the questions of system solution uniqueness and existence. Moreover, the question of consistent initial conditions, time series and solution in state space and phase space also deserve a great attention. Some of these questions, which do not exist when normal systems are treated, will be the subject of discussion in the sequel. These specific features of discrete descriptive systems can explain some of their unusual behaviors in transient responses. Some numerical examples have been worked out to illustrate the applicability of results presented.
Key words: linear systems, discrete descriptive systems, existence and uniqueness of solution, time series analysis, consistent initial conditions, discrete fundamental matrix.
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