Synchronization under matrix-weighted Laplacian

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 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.
Growth rate of switched homogeneous systems
Tuna, Sezai Emre (Elsevier BV, 2008-11-01)
We consider discrete-time homogeneous systems under arbitrary switching and study their growth rate, the analogue of joint spectral radius for switched linear systems. We show that a system is asymptotically stable if and only if its growth rate is less than unity. We also provide an approximation algorithm to compute growth rate with arbitrary accuracy.
Synchronization of small oscillations
Tuna, Sezai Emre (Elsevier BV, 2019-09-01)
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depend on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refi...
Quantitative measure of observability for linear stochastic systems
Subasi, Yuksel; Demirekler, Mübeccel (Elsevier BV, 2014-06-01)
In this study we define a new observability measure for stochastic systems: the mutual information between the state sequence and the corresponding measurement sequence for a given time horizon. Although the definition is given for a general system representation, the paper focuses on the linear time invariant Gaussian case. Some basic analytical results are derived for this special case. The measure is extended to the observability of a subspace of the state space, specifically an individual state and/or t...
Citation Formats
S. E. Tuna, “Synchronization under matrix-weighted Laplacian,” AUTOMATICA, pp. 76–81, 2016, Accessed: 00, 2020. [Online]. Available: