Finite time H∞ controller design based on finite time H∞ functional filter for linear continuous systems

In this paper we investigate the problem of the design of a controller based on H_∞ functional filter, in a finite time stability context for linear continuous time-invariant systems affected by norm bounded disturbances. The finite-time H_∞ boundedness criterion of the closed-loop system is investigated. The order of the controller is reduced since the designed functional filter has the same order than the dimension of the control input of the system. The design conditions are expressed as linear matrix inequalities. A numerical example is provided to show the validity of the proposed approach.