  Using any nonnegative function with a nonpositive derivative along
trajectories to define a virtual output, the classic LaSalle invariance
principle can be extended to switched nonlinear time-varying (NLTV) systems, by
considering the weak observability (WO) associated with this output. WO is what
the output informs about the limiting behavior of state trajectories (hidden in
the zero locus of the output). In the context of switched NLTV systems, WO can
be explored using the recently established framework of limiting zeroing-output
solutions. Adding to this, an extension of the integral invariance principle
for switched NLTV systems with a new method to guarantee uniform global
attractivity of a closed set (without assuming uniform Lyapunov stability or
dwell-time conditions) is proposed. By way of illustrating the proposed method,
a leaderless consensus problem for nonholonomic mobile robots with a switching
communication topology is addressed, yielding a new control strategy and a new
convergence result.
