Ultimate boundedness control of linear switched systems using controlled dwell time approach

Motivated by the satellite formation keeping control problem, this paper addresses the aspect of control design for the ultimate boundedness of linear switched systems consisting of both controlled (and thus stable) and uncontrolled (possibly unstable) subsystems. First, explicit formulae for the bounds on total activation times (or dwell times) in the controlled and uncontrolled modes are provided as a function of the parameters of the ellipsoidal ultimate boundedness region. A Lyapunov based control design scheme, called the controlled dwell time approach, is presented that achieves ultimate boundedness of the resulting switched system. The proposed design is illustrated with an example motivated by satellite formation keeping control problem