New Design of Robust LQR-State Derivative Controllers via LMIs

Abstract The resolution of linear quadratic regulator’s problem (LQR) approached via linear matrix inequalities (LMIs) for linear and time-invariant systems is proposed in this work. The design of the controllers is based on the state derivative feedback. The aim of the choice of the state derivative feedback is your easy implementation in a class of mechanical systems, such as in vibrations control, for example. The signals used for feedback are obtained by means of accelerometers. Still, in the controller design, the decay rate is considered. To illustrate the efficiency of the proposed theorems a practical implementation on an active suspension system is presented. During the implementation, an uncertainty in the model of the active suspension system and an actuator fault are assumed, and even in the presence of uncertainty and fault occurrence, the oscillations are attenuated by the proposed technique.