Stability analysis for nonlinear closed loop system structure

Abstract

In this paper, stability analysis is studied for the nonlinear closed loop system with a nonlinear plant and a nonlinear controller. Without the linearizing process for the nonlinear plant and the nonlinear controller, a Lipschitz continuous assumption of nonlinear plant is added and the notion of finite gain stability is defined. Then some inequalities about Lipschitz constants are derived to guarantee that the nonlinear system outputs are finite gain stability. To avoid the construction of the Lyapunov function, the convergence properties about the geometric series are applied to obtain two inequality conditions on the defined finite gain stability. Furthermore, one more complicated system, coming from engineering practice, is used to extend the nonlinear closed loop system, where the inner loop is applied to help another two controllers in achieving the desired tracking accuracy. Then the controller design for one flight simulation platform with six degrees of freedom confirms the theoretical results.

Keywords

• stability analysis
• nonlinear closed loop
• finite gain stability
• inequality condition
• lipschitz continuous