Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach

A new technique is proposed to construct observers and to achieve output feedback stabilization of a
class of continuous-time switched linear systems with a time-varying delay in the output. The delay is
a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative.
For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally
different from classical Lyapunov function based methods. A stability condition is given in terms of the
upper bound on the time-varying delay to ensure global uniform exponential stability of the switched
feedback system. The main result applies in cases where some of the subsystems of the switched system
are not stabilizable and not detectable.