Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

Máximo Ramírez; Raúl Villafuerte; Temoatzin González; Miguel Bernal

doi:10.1515/amcs-2015-0058

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Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

International Journal of Applied Mathematics and Computer Science

Volume 25 (2015): Issue 4 (December 2015)

By: Máximo Ramírez, Raúl Villafuerte, Temoatzin González and Miguel Bernal

Open Access

|Dec 2015

Abstract

This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

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