Stability of fuzzy gain-schedulers: sliding-mode based analysis

The design of a fuzzy gain scheduler requires a conventional model of the nonlinear system under control and a partition of the state space into a finite number of fuzzy regions. The nonlinear system is Lyapunov-linearized at the center of each fuzzy region. Then the linear controllers intended to locally stabilize the linearized system, and consequently the original nonlinear system, at the center of a fuzzy region are designed. With that, gain scheduling control of the original nonlinear system can be realized along a priori unknown, but slowly time varying desired trajectory. In this paper we analyse the stability and robustness of the gain scheduled closed loop system by adopting ideas from sliding mode control