Finite-time input-to-state stability and applications to finite-time control design

Yiguang Hong, Zhong Ping Jiang, Gang Feng

Research output: Contribution to journalArticlepeer-review


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, nonsmoothness 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.

Original languageEnglish (US)
Pages (from-to)4395-4418
Number of pages24
JournalSIAM Journal on Control and Optimization
Issue number7
StatePublished - 2010


  • Finite-time control
  • Input-to-state stability
  • Lyapunov functions
  • Nonsmooth feedback
  • Uncertainties

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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