On Stability Analysis of a Class of Nonlinear Systems with a Focus on Composite Nonlinear Feedback Approach

Abstract

Obtaining a desired transient performance of closed-loop system is the most important issues in impractical and industrial applications, in general. It is to note that the small overshoot and acceptable settling time of the system response are almost two typical characteristics in the transient performance. There are a number of contradictions between these performances; and therefore, a tradeoff between these ones should deeply be considered. In a word, a so-called composite nonlinear feedback (CNF) method is an efficient and simple technique which is employed to overcome the contradiction of simultaneous achievement of the mentioned transient performances. CNF based sliding mode control (SMC) for nonlinear systems with known upper bound uncertainty are considered in this paper. Unlike the existing results for the linear systems, the proposed CNF based SMC comprises two nonlinear parts. The first term assures the stability of the closed-loop nonlinear system and provides a fast convergence response. The second term reduces the overshoot of the response. Finally, to show the merits of the proposed approach, it is applied to two nonlinear Genesio's chaotic system and a nonlinear helicopter system. The investigated results verify the effectiveness of the proposed approach.

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