Stability of switched systems

[Braed]

I have a switched linear system and want to prove its asymptotic stability.
The system has the form [MATH]\dot{{x}}(t)={A}_{\sigma}\cdot{x}(t)+{B}_{\sigma}\cdot {u}(t)[/MATH] with constant coefficients.
Does somebody has any ideas?

 

[Deleted member 4993]

I have a switched linear system and want to prove its asymptotic stability.
The system has the form [MATH]\dot{{x}}(t)={A}_{\sigma}\cdot{x}(t)+{B}_{\sigma}\cdot {u}(t)[/MATH] with constant coefficients.
Does somebody has any ideas?

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[Braed]

I have made some assumptions: all the subsystems are asymptotically stable, the input signal and all [MATH]A_{\sigma} [/MATH] and [MATH]B_{\sigma}[/MATH] are known. I have read some sources and i know with a correct switching sequence , my system is stable. But the switching depends on x(t).
Now i was looking for stability independent from the switching signal and wanted to hear some ideas.
I hope this helps you to understand my problem better. Thank you.