Sergey Zubov

Ustoychivost' Raschetnykh Dvizheniy Sergey Zubov Russian edition

V nastoyashchey monografii rassmatrivaetsya vopros o povedenii resheniy sistem differentsial'nykh uravneniy v okrestnosti nekotorykh dvizheniy, kotorye mogut byt' tochnymi resheniyami etikh sistem, a mogut i ne byt' takovymi. V poslednem sluchae upomyanutye dvizheniya nosyat nazvaniya raschetnykh dvizheniy. Dlya sistem stabilizatsii programmnogo dvizheniya kh=0, yavlyayushchegosya raschetnym dvizheniem etikh sistem, privodyatsya dostatochnye usloviya vozniknoveniya v okrestnosti tochki kh=0 avtokolebaniy, t.e. zamknutykh, ogranichennykh, asimptoticheski ustoychivykh po Lyapunovu invariantnykh mnozhestv. Issleduetsya zadacha o sushchestvovanii i ustoychivosti sobstvennykh periodicheskikh dvizheniy sistem razlichnykh klassov (sistemy s gisterezisnymi nelineynostyami, dinamicheskaya sistema v metricheskom prostranstve, avtonomnaya sistema obyknovennykh differentsial'nykh uravneniy). V monografii razrabotany konstruktivnye kriterii i metody optimizatsii statsionarnykh sistem upravleniya, nablyudeniya i lineynoy stabilizatsii. Dlya lineynykh sistem, udovletvoryayushchikh uderzhivayushchim i ne uderzhivayushchim svyazyam, ustanovleny kriterii sushchestvovaniya i predlozheny analiticheskie metody postroeniya impul'snykh upravleniy i otvechayushchikh im dvizheniy. Prednaznacheno dlya nauchnykh rabotnikov.