Variable-Gain Controllers for Nonlinear Systems Using the T–S Fuzzy Model

This correspondence proposes two novel control schemes with variable state-feedback gain to stabilize a Takagi–Sugeno (T–S) fuzzy system. The T–S fuzzy model is expressed as a linear plant with nonlinear disturbance terms in both schemes. In controller I, the T–S fuzzy model is expressed as a linear plant around a nominal plant arbitrarily selected from the set of linear subsystems that the T–S fuzzy model consists of. The variable gain then becomes a function of a gain parameter that is computed to neutralize the effect of disturbance term, which is, in essence, the deviation of the actual system dynamics from the nominal plant as the system traverses a specific trajectory. This controller is shown to stabilize the T–S fuzzy model. In controller II, individual linear subsystems are locally stabilized. <emphasis emphasistype="italic">Fuzzy blending</emphasis> of individual control actions is shown to make the T–S fuzzy system Lyapunov stable. Although applicability of both control schemes depends on the norm bound of unmatched state disturbance, this constraint is relaxed further in controller II. The efficacy of controllers I and II has been tested on two nonlinear systems.