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Zbl 1210.93066
Hong, Yiguang; Jiang, Zhong-Ping; Feng, Gang
Finite-time input-to-state stability and applications to finite-time control design. (English)
[J] SIAM J. Control Optim. 48, No. 7, 4395-4418 (2010). ISSN 0363-0129; ISSN 1095-7138/e

Summary: This paper extends the well-known concept, Sontag's Input-to-State Stability (ISS), to finite-time control problems. In other words, a new concept, Finite-Time Input-To-State Stability (FTISS), is proposed and then is applied to both the analysis of finite-time stability and the design of finite-time stabilizing feedback laws of control systems. With finite-time stability, non-smoothness has to be considered, and serious technical challenges arise in the design of finite-time controllers and the stability analysis of the closed-loop system. It is found that FTISS plays an important role as the conventional ISS in the context of asymptotic stability analysis and smooth feedback stabilization. Moreover, a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of FTISS and related arguments.

MSC 2000:: *93D25 Input-output approaches to stability of control systems
93C10 Nonlinear control systems
34H15
93D15 Stabilization of systems by feedback

Keywords: finite-time control; input-to-state stability; nonsmooth feedback; Lyapunov functions; uncertainties

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