Global Exponential Stabilization for a Class of Uncertain Nonlinear Control Systems Via Linear Static Control

Yeong-Jeu Sun,Department Of Electrical Engineering, I-Shou University, Kaohsiung, Taiwan

doi:10.31142/ijtsrd20230

Yeong-Jeu Sun, Department Of Electrical Engineering, I-Shou University, Kaohsiung, Taiwan

Open Access

https://doi.org/10.31142/ijtsrd20230

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Abstract

Global Exponential Stabilization for a Class of Uncertain Nonlinear Control Systems Via Linear Static Control

Highlights

Control design with implementation of uncertain nonlinear dynamical systems is one of the most challenging areas in systems and control theory
Several numerical simulations will be provided to illustrate the use of the main results
We explore the following uncertain nonlinear systems: x&1 = ∆a1x1 + ∆a2 x2 + ∆a3x4 + ∆a4 x3x4, (1a) x&2 = ∆a5x1 + ∆a6 x2 + ∆a7 x3 + ∆a8 x4 + ∆a9 x1x3 + ∆a10u1, (1b) x&3 = ∆a11x2 + ∆a12 x3 − ∆a9 x1x2, (1c) x&4 = ∆a13x1 + ∆a14 x2 − ∆a4 x1x3 + ∆a15u2, (1d)

Summary

INTRODUCTION

Control design with implementation of uncertain nonlinear dynamical systems is one of the most challenging areas in systems and control theory. It is still difficult to implement nonlinear controllers for practical systems. The stabilizability for a class of uncertain nonlinear systems will been considered. Based on the Lyapunoe-like approach with differential inequality, a linear static control will be established to realize the global exponential stability of such uncertain systems. Several numerical simulations will be provided to illustrate the use of the main results. Rn denotes the n-dimensional real space, x denotes the Euclidean norm of the vector x ∈Rn , a denotes the absolute value of a real number a, and AT denotes the transport of the matrix A

RESULTS

NUMERICAL SIMULATIONS

CONCLUSION