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In this paper, we design a robust controller for rotary double inverted pendulum (RDIP) using linear matrix inequalities (LMIs) to stabilize the system regardless of some parametric uncertainties and input disturbances. In addition, the minimization of value of a given criterion function must be considered. The advantage of LMIs is that the design problem can be cast as convex problems such as an LMI minimization problem and a robust stability test of the closed-loop system. A state feedback Hinfin and an output feedback Hinfin controller will be proposed to solve the problem.