132 research outputs found
A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks
This paper presents a stability test for a class of interconnected nonlinear
systems motivated by biochemical reaction networks. One of the main results
determines global asymptotic stability of the network from the diagonal
stability of a "dissipativity matrix" which incorporates information about the
passivity properties of the subsystems, the interconnection structure of the
network, and the signs of the interconnection terms. This stability test
encompasses the "secant criterion" for cyclic networks presented in our
previous paper, and extends it to a general interconnection structure
represented by a graph. A second main result allows one to accommodate state
products. This extension makes the new stability criterion applicable to a
broader class of models, even in the case of cyclic systems. The new stability
test is illustrated on a mitogen activated protein kinase (MAPK) cascade model,
and on a branched interconnection structure motivated by metabolic networks.
Finally, another result addresses the robustness of stability in the presence
of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related
(p)reprint
Robust synchronization in networks of cyclic feedback systems
This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result
Circuit Model Reduction with Scaled Relative Graphs
Continued fractions are classical representations of complex objects (for
example, real numbers) as sums and inverses of simpler objects (for example,
integers). The analogy in linear circuit theory is a chain of series/parallel
one-ports: the port behavior is a continued fraction containing the port
behaviors of its elements. Truncating a continued fraction is a classical
method of approximation, which corresponds to deleting the circuit elements
furthest from the port. We apply this idea to chains of series/parallel
one-ports composed of arbitrary nonlinear relations. This gives a model
reduction method which automatically preserves properties such as incremental
positivity. The Scaled Relative Graph (SRG) gives a graphical representation of
the original and truncated port behaviors. The difference of these SRGs gives a
bound on the approximation error, which is shown to be competitive with
existing methods.Comment: Submitted to CDC202
Secant and Popov-like Conditions in Power Network Stability
The problem of decentralized frequency control in power networks has received an increasing attention in recent years due to its significance in modern power systems and smart grids. Nevertheless, generation dynamics including turbine-governor dynamics, in conjunction with nonlinearities associated with generation and power flow, increase significantly the complexity in the analysis, and are not adequately addressed in the literature. In this paper we show how incremental secant gain conditions can be used in this context to deduce decentralized stability conditions with reduced conservatism. Furthermore, for linear generation dynamics, we establish Popov-like conditions that are able to reduce the conservatism even further by incorporating additional local information associated with the coupling strength among the bus dynamics. Various examples are discussed
throughout the paper to demonstrate the significance of the results presented.ER
Secant Conditions in Power Network Stability
© 2018 European Control Association (EUCA). The problem of decentralized frequency control in power networks has received an increasing attention in recent years due to its significance in modern power systems and smart grids. Nevertheless, generation dynamics often involve turbine/governor dynamics, which, in conjunction with non-linearities associated with generation and power flow, increase significantly the complexity in the analysis, and are not adequately addressed in the literature. In this paper we show how incremental secant gain conditions can be used in this context to reduce the conservatism in the analysis. The stability conditions derived are decentralized and are demonstrated throughout the paper with various examples.ERC starting grant 67977
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