Fuzzy singularly perturbed modeling and composite controller design for nonlinear multiple time-scale systems with time-delay

This paper investigates the problems of modeling and robust controller design for nonlinear multiple time-scale systems (MTSSs) with time-delay. An uncertain standard discrete-time fuzzy singularly perturbed model (FSPM) with time-delay is firstly constructed to estimate the considered system. Based on a matrix spectral norm approach, robust composite controllers with or without time-delay are designed respectively. They are composed by a slow-state-variables feedback controller and an output integrator. The controller's gains are obtained by solving a set of ε-independent linear matrix inequalities (LMIs) such that the ill-conditioned problems caused by ε can be easily avoided. The designed control laws not only can stabilize resulting closed-loop systems but also can overcome external disturbances. Finally, simulation results for CE150 helicopter system illustrate the effectiveness of the proposed approaches. In contrast to the existing results, the proposed methods have the following advantages: i) They have better practical value since parameter uncertainty, external disturbances and the problem that the state variables are not fully measurable are considered. ii) A high accurate control performance can be achieved. iii) External disturbances can be effectively reduced.