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Abstract
This paper proposes two kinds of nonlinear general integral controllers, that is, one is generic and another is practical, for a class of uncertain nonlinear system. By extending equal ratio gain technique to a canonical interval system matrix and using Lyapunov method, theorems to ensure regionally as well as semi-globally asymptotic stability are established in terms of some bounded information. Moreover, for the practical nonlinear integral controller, a real time method to evaluate the equal ratio coefficient is proposed such that its value can be chosen moderately. Theoretical analysis and simulation results demonstrated that not only nonlinear general integral control can effectively deal with the uncertain nonlinear system but also equal ratio gain technique is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions.
Highlights
Integral control [1] plays an important role in practice because it ensures asymptotic tracking and disturbance rejection when exogenous signals are constants or planting parametric uncertainties appears
For the practical nonlinear integral controller, a real time method to evaluate the equal ratio coefficient is proposed such that its value can be chosen moderately
Theoretical analysis and simulation results demonstrated that nonlinear general integral control can effectively deal with the uncertain nonlinear system and equal ratio gain technique is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions
Summary
Integral control [1] plays an important role in practice because it ensures asymptotic tracking and disturbance rejection when exogenous signals are constants or planting parametric uncertainties appears. Equal ratio gain technique firstly was proposed by [10], and was used to address the linear general integral control design for a class of uncertain nonlinear system. All these general integral controllers above constitute only a minute portion of general integral control, and lack generalization. Theoretical analysis and simulation results demonstrated that nonlinear general integral control can effectively deal with the uncertain nonlinear system and equal ratio gain technique is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions.
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