Basics of Linear Systems

  • Marat Akhmet


We start discussion of linear impulsive systems with the following differential equation:
$$\begin{array}{rcl} & & x^\prime = A(t)x, \\ & & \Delta x{\vert }_{t={\theta }_{i}} ={B}_{i}x,\end{array}$$
where \((t,x) \in \mathbb{R} \times {\mathbb{R}}^{n},{\theta }_{i},i \in \mathbb{Z},\) is a B-sequence, such that | θ i | → as | i | → . We suppose that the entries of n ×n matrix A(t) are from \(\mathcal{P}C(\mathbb{R},\theta ),\) real valued n ×n matrices \({B}_{i},i \in \mathbb{Z},\) satisfy
$$\det (\mathcal{I} + {B}_{i})\not =0,$$
where \(\mathcal{I}\) is the identical n ×n matrix.


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© Springer New York 2010

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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