Relaxed stability criteria for discrete-time Takagi–Sugeno fuzzy systems via new augmented nonquadratic Lyapunov functions

• An augmented nonquadratic Lyapunov function is proposed.
• The criterion takes the form of an LMI which is computationally tractable.
• The obtained stability criteria are less conservative.
• The existing results are special cases of ours.

The problem of relaxed stability analysis of discrete-time Takagi–Sugeno fuzzy systems is investigated in this paper. Different from those existing results in the literature that are only quadratic parameter dependent on system state variables, a new augmented nonquadratic Lyapunov function, which is formulated in a higher order form of system state variables than those existing results, is developed for achieving the task of stability analysis with less conservatism. More importantly, it can be proved that the approach proposed in this paper contains the existing one as a special case. Finally, the effectiveness of the proposed approach is illustrated by means of numerical experiments.