Filter design for discrete-time singularly perturbed T–S fuzzy systems

This paper investigates the H ∞ filtering problem for a class of nonlinear discrete-time singular systems described by Takagi–Sugeno (T–S) fuzzy singular model with time-delay. By employing the Lyapunov–Krasovskii approach and the free-weighting matrix technique, a delay-dependent criterion is established in terms of linear matrix inequality (LMI), which ensures the concerned system to be regular, causal and stable with an H ∞ performance. Moreover, a sufficient condition for the existence of the desired H ∞ filters is also established. Two numerical examples are given to illustrate the effectiveness of the proposed theories.