From b495972812bde685da4b577965f58546acc7f25e Mon Sep 17 00:00:00 2001 From: Petr Velycko Date: Thu, 15 May 2025 09:04:29 +0200 Subject: [PATCH] optimalizace struktury --- ljapunovske-funkce.tex | 1 - skripta.pdf | Bin 207782 -> 207797 bytes 2 files changed, 1 deletion(-) diff --git a/ljapunovske-funkce.tex b/ljapunovske-funkce.tex index f81d0cd..54bc004 100644 --- a/ljapunovske-funkce.tex +++ b/ljapunovske-funkce.tex @@ -74,7 +74,6 @@ K důkazu této věty budeme potřebovat následující lemma o zachovávání k a tedy $V(x(t_n), t_n) \to 0$. Díky větě o limitě podposloupnosti dostáváme, že $V(x(t), t) \to 0 = a$ a jelikož $0 \leq \omega(x(t)) \leq V(t, x(t)) \to 0$, musí nutně platit $\omega(x(t)) \to 0$. Jelikož posloupnost $t_n$ byla volena libovolně, máme díky předchozímu lemmatu $x(t_n) \to 0$ pro libovolnou $t_n \nearrow +\infty$, a tedy dle Heineovy věty $x(t) \to 0$, což jsme chtěli dokázat. - \end{proof} Na závěr si uvedeme větu, která nám poskytuje několik možných charakterizací pro asymptotickou stabilitu nulového řešení. diff --git a/skripta.pdf b/skripta.pdf index 755368aa4367ae30194496d7e98d765b65ad3fb2..95b701b5433e2df679dd266ab5d6f2cc2892426b 100644 GIT binary patch delta 19539 zcmY&;LvSSwux@PIwl&ejw(U%88z;7PV%xTD+jcS&JGp<=yNh=>-M#7Ru3oghuXGKe zWep*q85Fq=lqWfnl@h?i%_blK=i=&YW^4!Nxp~7s6-UA4{PGo*6aeX6U(SI$aMrmJ zfUpk#(fYg&tt}wuAtvMbohz2NO_8pVVsq5d>rLYUVV%y0Yq68 z^j$1vpF6yloq%iMiMEA;cAAGc9v;BVE~qzONtqo=c@|$KNdBwrfBWEOpEI(8dP?6t zd_%lb1r@|Uvjpr7Dvl5?!o-lLM(4eCa(dMvK3WbJ_S8G?RLg>cUIwNaRh2LeEvv4F zVtGkgfCfMq5BRW>?H;tSn+|>-z5mJs;pYkB%PC31qw5bh{`ur2^kv7%(dx&&;H0iI zeqrqiXz>0>!L{FJ*p+D-437^JniGZ185W5!UOAvSIRvz%amF^1Im|aJiSaVvQ+Iu6 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