Switching topology means that the topology of the agents switch into a different topology over time. Time-varying formation happens when the formation pattern changes over time for several different reasons. Can we interpret that topology switching is a unavoidable consequential step in time-varying formation?
Check this links may be the papers are useful for your question
https://tel.archives-ouvertes.fr/tel-01415332/document
https://www.researchgate.net/publication/226887365_Consensus_tracking_protocol_and_formation_control_of_multi-agent_systems_with_switching_topology
I think switching topology case can be considered as a subset of time-varying formation/consensus. Consider the following two cases for discrete time consensus:
(i) When the topology of a network is switching, the system matrix W[k] (row-stochastic for discrete-time) will be different for some k>0 such that w_ij[k] > 0 does not mean w_ij[k'] > 0 for some k' ≠ k.
(ii) Suppose that topology is fixed but agents of a network use different weights for some k that results in time-varying system matrix W[k]. In that case, if w_ij[k] > 0 holds, then we have w_ij[k'] > 0 for some k' ≠ k.
Similar arguments are also valid for Laplacian matrix L(t) (zero row sum for cont. time). Hence, while (i) represents the switching topology case, time-varying formation/consensus case might be represented either (i) or (ii) depending on the problem.
Hope this helps.
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