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Using any nonnegative function with a nonpositive derivative alongtrajectories to define a virtual output, the classic LaSalle invarianceprinciple can be extended to switched nonlinear time-varying (NLTV) systems, byconsidering the weak observability (WO) associated with this output. WO is whatthe output informs about the limiting behavior of state trajectories (hidden inthe zero locus of the output). In the context of switched NLTV systems, WO canbe explored using the recently established framework of limiting zeroing-outputsolutions. Adding to this, an extension of the integral invariance principlefor switched NLTV systems with a new method to guarantee uniform globalattractivity of a closed set (without assuming uniform Lyapunov stability ordwell-time conditions) is proposed. By way of illustrating the proposed method,a leaderless consensus problem for nonholonomic mobile robots with a switchingcommunication topology is addressed, yielding a new control strategy and a newconvergence result.

Invariance Principles and Observability in Switched Systems with an Application in Consensus