Delayed state feedback controller design for inverted pendulum using T-S fuzzy modeling: An LMI approach

Abstract

Balancing inverted pendulum along a vertical position with or without cart is a benchmark control problem owing to the fact that out of two equilibrium points, inverted one is open-loop unstable. In this paper, an attempt has been made to stabilize the system with delayed state feedback control strategy using T-S fuzzy modeling in an linear matrix inequality (LMI) framework. Then, by Lyapunov–Krasovskii (L-K) theory, it is proved that the closed-loop system is locally asymptotically stable around its unstable equilibrium point. The result of the control design is validated through closed-loop simulation carried out in MATLAB Simulink.