Control of nonlinear discrete-time systems subject to energy bounded disturbances using local T-S fuzzy models

This paper addresses the input-to-state stabilization problem in the ℓ
₂
sense for a class of discrete-time nonlinear systems described by Takagi-Sugeno (T-S) fuzzy models. It turns out that T-S models accurately represent the original system in some bounded region of the state space (namely the T-S domain of validity). Thus, a numerical and tractable solution to the local stabilization problem is proposed while providing an estimate of the closed-loop stability region (a positively invariant set belonging to the T-S domain of validity which bounds the state trajectory driven by admissible disturbance inputs). This paper concentrates on the state feedback design problem in which the feedback gain is computed by means of a convex optimization problem in terms of linear matrix inequality constraints. Numerical examples illustrate the technique demonstrating the effectiveness of the approach as a control design tool for nonlinear discrete-time systems.