Growth rate of switched homogeneous systems

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.

Suggestions

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.
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...
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 ...
Spherical wave expansion of the time-domain free-space Dyadic Green's function
Azizoglu, SA; Koç, Seyit Sencer; Buyukdura, OM (Institute of Electrical and Electronics Engineers (IEEE), 2004-03-01)
The importance of expanding Green's functions, particularly free-space Green's functions in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time-domain scattering problems, similar expansions of Green's functions are expected to be useful in the time-domain. In this paper, an expression, expanded in terms of orthogonal spherical vector wave functions, for the time-domain free-space...
BLOCH IMPEDANCE ANALYSIS FOR A LEFT HANDED TRANSMISSION LINE
Sabah, Cumali; Urbani, Fabio; Uckun, Savas (Walter de Gruyter GmbH, 2012-09-01)
In this study, the dispersion relation and the frequency dependence of Bloch impedance in a left handed transmission line (LH-TL) is carried out using the F-matrix formulation and Bloch-Floquet theorem. The artificial LH-TL formed by periodic lumped elements is described and the F-matrix, dispersion relation and the Bloch impedance are formulated according to this description. Numerical results for lossless and lossy LH-TL are presented and discussed.
Citation Formats
S. E. Tuna, “Growth rate of switched homogeneous systems,” AUTOMATICA, pp. 2857–2862, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48981.