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-1 39 "To verify V(x,y) is a Lyapunov function" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 "
Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warni
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0 14 "f:=-x^3+x*y^2;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "g:=-x^2*y-y^3;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "V:=y^2+x^2;" }}{PARA 11 "" 1 "" 
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x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Vy:=diff(V,y);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "1) To prove " }{TEXT 260 1 "V" }
{TEXT -1 1 "(" }{TEXT 261 3 "x,y" }{TEXT -1 19 ") positive definite" }
}{PARA 0 "" 0 "" {TEXT -1 6 "Since " }{OLE 1 3586 1 "[xm]Br=WfoRrB:::w
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::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ND
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:::::::::::::::::::::::::::::1:" }{TEXT -1 6 " and  " }{OLE 1 3586 1 "
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yyqy;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::NDYmq^H;C:ELq^H_mvJ::::::::gj<vyyuyJ<j?V:;J:>R<:T><::;h
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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::=Z<Z:::>xun
<[kZFB[KRF@GlSF@gKVfI>d:FFAmoFFIml^A^Z;r:Eb<=b>AVXAr=V[KFZ<>klZ:::::::
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MR<JRJ:<:::::::>=?R:J;>:yayA:;B::::::^:;JmAZ:B:N:Y<>DjsJRJ:<:::::::>=;
jysy:>:<::::::wqy[:::::::::::::vYxI:;Z::::::::::::::::::::yay=J:B:::::
:::jP@:MB:;B:_c<;W:kl:>Z:Fis?Os:qQJxI<:[V:;Z:b:<;:::JyHJ?L@O:<jPF:CB:>
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JmHv=Nk;J?n:v:O>^:f?;J<JrG:AB:<J::::::::::::::::::::::::::::::::::::::
:::::::::::::5:" }{TEXT -1 33 "are both greater than 0 for all (" }
{TEXT 262 3 "x,y" }{TEXT -1 24 ") other than (0,0) then " }{TEXT 263 
1 "V" }{TEXT -1 1 "(" }{TEXT 264 3 "x,y" }{TEXT -1 13 ")>0 for all (" 
}{TEXT 265 3 "x,y" }{TEXT -1 23 ") other than (0,0) and " }{TEXT 266 
1 "V" }{TEXT -1 7 "(0,0)=0" }}{PARA 0 "" 0 "" {TEXT -1 6 "Thus V" }
{TEXT 256 1 "(" }{TEXT -1 3 "x,y" }{TEXT 257 2 ") " }{TEXT -1 21 "is p
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