On switched control design of linear time-invariant systems with polytopic uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure. © 2013 Wallysonn A. de Souza et al.

Keywords

Feedback controller, Linear matrix inequality (LMIs), Linear time invariant systems, Magnetic levitator, Polytopic uncertainties, Quadratic lyapunov function, State feedback gain, Switched control, Linear matrix inequalities, Lyapunov functions, Switching systems, Time varying control systems, Control