Adaptive Fuzzy Output-Feedback Control for Switched Nonlinear Systems With Stable and Unstable Unmodeled Dynamics

Dynamic uncertainty is a potential factor destabilizing the closed-loop system. This paper aims at constructing an adaptive fuzzy output-feedback control scheme for a class of switched nonlinear systems interconnected with unmodeled dynamics. In the investigated model, the x-system is interconnected with the unmodeled z-dynamics. Two types of unmodeled dynamics (i.e., all modes are stable and some modes are unstable) are considered in this paper. Separate switched state observer and adaptive fuzzy controller are designed for each mode of the x-system. In our control scheme, only two adaptive parameters are required to update online. With the help of multiple Lyapunov function, two lemmas are proposed to guide us how to determine the input-to-output gains of the x-system and the unmodeled dynamics when the influence of switching is considered. By using the small-gain approach, the closed-loop switched nonlinear system is guaranteed to be of input-to-state practically stability (ISpS). With the concept of ISpS, we prove that the closed-loop system's output is convergent to a small neighborhood of zero, and all the signals in the closed-loop system are bounded. Finally, three simulations are also given to illustrate the effectiveness of our main result.