Local stability and stabilization of uncertain nonlinear systems with two additive time-varying delays

Abstract

Abstract This paper investigates the local stability and stabilization problem of nonlinear time-delay systems subject to parameter uncertainties, which are represented by interval type-2(IT2) T-S fuzzy systems with two additive time-varying delays. Because T-S fuzzy models often represent primitive nonlinear systems well only in the region of validity, local stability and stabilization problems are considered. By constructing a novel Lyapunov–Krasovskii functional and using the matrix inequality scaling approach, a new delay-dependent local stability and stabilization criterion is derived in terms of linear matrix inequalities(LMIs). Using Lyapunov level set, the estimation of attraction domain is also developed. Finally, two numerical examples are employed to verify the effectiveness of proposed methods.