On the stability of a class of nonlinear control systems

Abstract

In this paper, the stability of a class of nonlinear control systems is analyzed. This class of systems is first converted into the equivalent affine control systems using the linear combination property of intervals where it is utilized to convert the nonlinear control systems into the equivalent linear control systems in works (Noori Skandari and Tohidi in Appl Math 2:646–652, 2011; Erfanian et al. in Int J Sens Comput Control 1(2):117–124, 2011; Tohidi and Noori Skandari in J Comput Model 1(2):145–156, 2011). Then to analyze the stability of the obtained affine control system, two analytical approaches based on the scalar and vector control Lyapunov functions are utilized and a control stabilizer is constructed. Finally, the results are simulated in some examples.