Synchronizing linear systems via partial-state coupling

A basic result in the synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their Outputs and neutrally stable, it is shown that a linear Output feedback law exists under which the Coupled systems globally asymptotically synchronize for all fixed connected (asymmetrical) network topologies. An algorithm is provided to Compute Such a feedback law based on individual system parameters.


Conditions for Synchronizability in Arrays of Coupled Linear Systems
Tuna, Sezai Emre (2009-10-01)
Synchronization in arrays of coupled continuous-time linear systems is studied. Sufficiency of certain conditions for the existence of a synchronizing feedback law are analyzed. It is shown that, for neutrally stable systems that are detectable from their outputs, a linear feedback law exists under which any number of coupled systems synchronize provided that the (directed, weighted) graph describing the interconnection is fixed and connected. An algorithm generating one such feedback law as well as the tra...
Synchronization under matrix-weighted Laplacian
Tuna, Sezai Emre (Elsevier BV, 2016-11-01)
Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain for each pair of systems, which ensures that all the solutions converge to a common trajectory.
Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks
Tuna, Sezai Emre (2017-01-01)
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented. Through simple physical examples, the meaning and limitations of the theorems are expounded. Also, to demonstrate their versatility, the results are extended to cover LTI passive electrical networks. One of the extensions generalizes the well-known link between the asymptoti...
Synchronization of linear oscillators coupled through a dynamic network with interior nodes
Tuna, Sezai Emre (Elsevier BV, 2020-07-01)
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix ...
Synchronization of linear systems via relative actuation
Tuna, Sezai Emre (Elsevier BV, 2019-12-01)
Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via dynamic relative output feedback is presented.
Citation Formats
S. E. Tuna, “Synchronizing linear systems via partial-state coupling,” AUTOMATICA, pp. 2179–2184, 2008, Accessed: 00, 2020. [Online]. Available: