Adding an integrator and uniform ISS stabilization for switched MIMO triangular systems with unknown switched signal and right invertible input-output maps
نویسندگان
چکیده
We extend some recent (2009,2010) results devoted to the Lyapunov stabilization for the switched systems in the strict-feedback form. More speci cally, we prove that a multi-input and multi-output triangular switched system with an unknown switching signal, with right-invertible input-output links, and with dynamics, which is a ne in external disturbances is globally uniformly input-to-state stabilizable with respect to the disturbances. Ñ. Äàøêîâñüêèé, Ñ.Ñ. Ïàâëè÷êîâ. Îáõiä iíòåãðàòîðà i ðiâíîìiðíà ñòàáiëiçàöiÿ âõiä-ñòàí òðèêóòíèõ ñèñòåì ç ïåðåìiêàííÿìè ç áàãàòüìà âõîäàìè i âèõîäàìè, ç íåâiäîìèìè ïåðåìèêàííÿìè i ç ïðàâîîáîðîòíèìè âiäîáðàæåííÿìè âõiä-âèõiä. Ó ðîáîòi óçàãàëüþþòüñÿ äåÿêi íîâi (2009,2010) ðåçóëüòàòè, ÿêi ïðèñâÿ÷åíi ñòàáiëiçàöi ̈ çà Ëÿïóíîâèì ñèñòåì ç ïåðåìèêàííÿìè òðèêóòíîãî âèãëÿäó. Òî÷íiøå, ìè äîâîäèìî, ùî òðèêóòíi ñèñòåìè ç ïðàâîîáîðîòíèìè âiäîáðàæåííÿìè âõiä-âèõiä i ç ïðàâèìè ÷àñòèíàìè àôiííèìè ùîäî çîâíiøíiõ çáóðåíü ðiâíîìiðíî ñòàáiëiçóþòüñÿ çà âõîäîì-ñòàíîì âiäíîñíî çáóðåíü. Ñ. Äàøêîâñêèé, Ñ.Ñ. Ïàâëè÷êîâ. Îáõîä èíòåãðàòîðà è ðàâíîìåðíàÿ ñòàáèëèçàöèÿ âõîä-ñîñòîÿíèå òðåóãîëüíûõ ñèñòåì ñ ïåðåêëþ÷åíèÿìè ñî ìíîãèìè âõîäàìè è âûõîäàìè, ñ íåèçâåñòíûìè ïåðåêëþ÷åíèÿìè è ñ ïðàâîîáðàòèìûìè îòîáðàæåíèÿìè âõîä-âûõîä.  ðàáîòå îáîáùàþòñÿ íåêîòîðûå íîâûå (2009,2010) ðåçóëüòàòû, ïîñâÿùåííûå ñòàáèëèçàöèè ïî Ëÿïóíîâó ñèñòåì ñ ïåðåêëþ÷åíèÿìè òðåóãîëüíîãî âèäà. Áîëåå òî÷íî, ìû äîêàçûâàåì, ÷òî òðåóãîëüíûå ñèñòåìû ñ íåèçâåñòíûìè ïåðåêëþ÷åíèÿìè, ñ ìíîãèìè âõîäàìè è âûõîäàìè, ñ ïðàâîîáðàòèìûìè îòîáðàæåíèÿìè âõîä-âûõîä è ñ ïðàâûìè ÷àñòÿìè àôôèííûìè îòíîñèòåëüíî âíåøíèõ âîçìóùåíèé ðàâíîìåðíî ñòàáèëèçèðóåìû ïî âõîäó-ñîñòîÿíèþ îòíîñèòåëüíî âîçìóùåíèé. 2000 Mathematics Subject Classi cation 93C10, 93B10, 93B11, 93B05, 93B52.
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