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Dynamic analysis of linear singular systems using orthogonal functions
Dragutin Lj. Debeljković Mića B. Jovanović Vesna Drakulić Dušan J. Đekić
Singular 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 to the solution of the differential part. These systems, also known as descriptor, semi-state and generalized systems, arise naturally as a linear approximation of system models, or linear system models in many applications such as electric networks, aircraft dynamics, neural delay systems, chemical, thermal and diffusion processes, large-scale systems, interconnected systems, economics, optimization problems, feedback systems, robotics, biology, etc. For an elementary dynamic analysis of singular systems their solution in state space is necessary. In classical sense it means that there is a need for calculating general or pseudo inversions of system matrices. On the other hand this is too complicated in numerical sense. So this paper investigates another possibility of solving system equations using different aproximations based on strict applications of very well-known orthogonal functions. Some numerical examples have been worked out to show the applicability of the presented results.
Key words:
linear singular systems, dynamic analysis, orthogonal functions. |