Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

Abstract

SummaryThis paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.