Ib lub sij hawm-invariant system yog asymptotically ruaj khov yog tias tag nrho cov eigenvalues ntawm lub system matrix A muaj qhov tsis zoo tiag tiag. Yog tias lub kaw lus yog asymptotically ruaj khov, nws kuj yog BIBO ruaj khov.
Yuav ua li cas rau asymptotically ruaj khov ntawm lub hauv paus chiv keeb?
Yog V (x, t) yog lub hauv paus zoo meej thiab decrescent, thiab − ˙V (x, t) yog lub hauv paus zoo meej, ces lub hauv paus ntawm lub system yog uniformly hauv zos asymptotically ruaj khov.
Qhov txawv ntawm qhov ruaj khov thiab asymptotically ruaj khov yog dab tsi?
txhais tau li cas thaum qhov sib npaug ntawm qhov sib npaug yog "ruaj khov" piv rau thaum qhov sib npaug taw tes yog "asymptotically ruaj khov." Lub ntsiab lus sib npaug tau hais tias yog asymptotically ruaj khov yog tias qee qhov pib tus nqi ze rau qhov sib npaug ntawm qhov sib npaug, qhov kev daws teeb meem yuav hloov mus rau qhov qhov sib npaug.
Koj txiav txim siab li cas yog tias qhov system yog Lyapunov ruaj khov?
1. Yog V (x, t) yog lub hauv paus zoo meej thiab ˙V (x, t) ≤ 0 hauv x thiab rau tag nrho t, ces lub hauv paus ntawm lub system yog nyob ruaj khov (hauv lub siab ntawm Lyapunov). 2.
Puas yog keeb kwm asymptotically ruaj khov?
tag nrho lub xeev qhov chaw, ces qhov sib npaug ntawm lub hauv paus chiv keeb yog globally asymptotically ruaj khov.
