Neuro-fuzzy tracking control of discrete-time nonlinear systems under Linear Matrix Inequality region constraints

This study investigates the problem of system identification and control for non-affine nonlinear deterministic systems using a generalised state-space neuro-fuzzy model. The proposed new model consists of a seven-layer neural network, where the consequent part comprises a finite set of discrete-time invariant linear state-space models. For tracking control design, quadratic stabilisers are integrated within a Parallel Distributed Compensation framework. Instead of merely ensuring the closed-loop stability of the state-augmented system, the feedback matrices are computed by solving a region-constrained Linear Matrix Inequality problem, which guarantees that the closed-loop eigenvalues remain within a D -stable region. The proposed generalised neuro-fuzzy model is proven to be a universal approximator on compact sets, with sufficient conditions for closed-loop stability established under the Neuro-Fuzzy-based Parallel Distributed Compensation framework. Experimental results on a nonlinear benchmark system validate the effectiveness and practical feasibility of the proposed neuro-fuzzy tracking control strategy.