Mixed sliding mode fuzzy control for discrete-time non-linear stochastic systems subject to variance and passivity constraints

In this study, a novel multi-objective sliding mode fuzzy control technique is presented for a class of discrete-time non-linear stochastic systems that are represented by Takagi-Sugeno (T-S) fuzzy models. Subject to variance and passivity constraints, parallel distributed compensation based sliding mode fuzzy control approach is investigated for the discrete-time T-S fuzzy models. Combining Lyapunov theory, passivity theory and covariance theory, sufficient conditions are derived to satisfy stability, passivity and variance constraints. The iterative linear matrix inequality algorithm is employed in this study to solve these sufficient conditions. The contribution of this study is to develop a novel sliding mode fuzzy control method such that the closed-loop discrete-time non-linear stochastic system achieves passivity constraint and individual state variance constraints, simultaneously. At last, the simulations of controlling a discrete-time non-linear ship steering system are given in a numerical example to demonstrate the effectiveness and usefulness of proposed sliding mode fuzzy control methodology.