Sontag, Eduardo D.; Wang, Yuan New characterizations of input-to-state stability. (English) Zbl 0862.93051 IEEE Trans. Autom. Control 41, No. 9, 1283-1294 (1996). This paper studies some stability properties of the state response with respect to inputs of smooth nonlinear systems of the form \[ \dot x=f(x,u). \] The starting point is the so-called ISS property. This means that the norm of the solution is majorized at each future time \(t\) by an expression \(\beta(|\xi|,t)+\gamma(|u|)\), where \(\xi\) is the initial state, \(|u|\) is the \(L_\infty\) norm of the input and \(\beta\), \(\gamma\) are suitable comparison function.The authors introduce a list of (apparently different) properties which are in fact proved to be equivalent to ISS. This variety of possible formulations turns out to be useful in several applications. Reviewer: A.Bacciotti (Torino) Cited in 207 Documents MSC: 93D25 Input-output approaches in control theory 93C10 Nonlinear systems in control theory Keywords:input/output behaviour; Lyapunov methods; nonlinear systems PDFBibTeX XMLCite \textit{E. D. Sontag} and \textit{Y. Wang}, IEEE Trans. Autom. Control 41, No. 9, 1283--1294 (1996; Zbl 0862.93051) Full Text: DOI Link