Brief Introduction to Linear System Theory




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The purpose of this paper is to provide the reader with basics of linear system theory. We consider a system given by ordinary differential equation of n-th order. We show its transformation into the state equation (system of equations). Next, we study existence of solution of state equation and its stability. We also explain notions of controllability, observability and realizability. Finally we study linear feedback and its effect on stability. In the paper mostly systems with constant coefficients are considered, but we try to give a comparison with time-varying case when necessary or interesting. The explanation is brief, but the purpose is to offer short introduction to the reader that has some background in mathematics, but basically no knowledge of system theory.