Stability of Nonautonomous Systems by Liapunov’s Direct Method
نویسندگان
چکیده
This paper discusses asymptotic stability for nonautonomous systems by means of the direct method of Liapunov. The existence of a positive time-invariant Liapunov function with negative semi-definite derivative is assumed. The paper focuses on the extra conditions needed in order to guarantee asymptotic stability. The proposed criterion is compared with the standard results available for autonomous systems. A specialization and extension is obtained for a class of linear nonautonomous systems.
منابع مشابه
Dynamic Systems and Applications 14 (2005) 525-550 NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY IN VOLTERRA EQUATIONS OF NONCONVOLUTION TYPE
Necessary and sufficient conditions for asymptotic stability in linear Volterra equations of nonconvolution type are established by Liapunov’s direct method. A comparison theorem for nonlinear delay systems is also proved by means of linear integrodifferential inequalities. AMS (MOS) Subject Classification. 34K20, 34D20.
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تاریخ انتشار 2013