Basics of Linear Systems

Marat Akhmet ()
Additional contact information
Marat Akhmet: Middle East Technical University, Department of Mathematics

Chapter Chapter 4 in Principles of Discontinuous Dynamical Systems, 2010, pp 31-54 from Springer

Abstract: Abstract We start discussion of linear impulsive systems with the following differential equation: 4.1 $$\begin{array}{rcl} & & x^\prime = A(t)x, \\ & & \Delta x{\vert }_{t={\theta }_{i}} ={B}_{i}x,\end{array}$$ 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 4.2 $$\det (\mathcal{I} + {B}_{i})\not =0,$$ where $$\mathcal{I}$$ is the identical n ×n matrix.

Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6581-3_4

Ordering information: This item can be ordered from
http://www.springer.com/9781441965813

DOI: 10.1007/978-1-4419-6581-3_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().