Distributed robust stability analysis of interconnected uncertain systems

Andersen, Martin S.; Hansson, Anders; Pakazad, Sina Khoshfetrat; Rantzer, Anders

doi:10.1109/cdc.2012.6426306

Cited by 14 publications

(35 citation statements)

References 34 publications

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“…Consider the same NS Σ investigated in [1], [17]. This system is constituted from N linear time invariant (LTI) dynamic subsystems and the dynamics of its i-th subsystem Σ i is described by the following state space model…”

Section: System Description and Some Preliminariesmentioning

confidence: 99%

“…Note also that approximate power-law degree distribution exists extensively in science and engineering systems, such as gene regulation networks, protein interaction networks, internet, electrical power systems, etc. For these systems, interactions among subsystems are sparse and the matrix Φ usually has a dimension significantly smaller than that of its state vector [1], [9], [6], [17]. Under such a situation, results of this paper work well in general.…”

Section: System Description and Some Preliminariesmentioning

confidence: 99%

“…With the same concept, a sufficient condition has been derived in [1] for the robust stability of a NS.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we reinvestigate stability of the NS adopted in [1], [17]. A necessary and sufficient condition has been derived which explicitly takes system structures into account.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Stability and Robust Stability of Networked Dynamic Systems

Zhou

Zhang

2016

IEEE Trans. Automat. Contr.

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Some necessary and sufficient conditions are derived for the stability of a networked system with linear time invariant dynamics. Connections among its subsystems are fixed but arbitrary, and every subsystem can have different dynamics. Based on these results, some necessary or sufficient conditions are further obtained for both its stability and robust stability, which essentially depend only on parameter matrices of each individual subsystem and the subsystem connection matrix. This characteristic makes them attractive in the analysis and synthesis of a large scale networked system.

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Section: System Description and Some Preliminariesmentioning

confidence: 99%

Section: System Description and Some Preliminariesmentioning

confidence: 99%

“…With the same concept, a sufficient condition has been derived in [1] for the robust stability of a NS.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we reinvestigate stability of the NS adopted in [1], [17]. A necessary and sufficient condition has been derived which explicitly takes system structures into account.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Stability and Robust Stability of Networked Dynamic Systems

Zhou

Zhang

2016

IEEE Trans. Automat. Contr.

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“…We have chosen a simple example to demonstrate what can be done if (12) happens to be sparse in order to not clutter the presentation. The general case can be handled similarly as is described for a centralized solution in Andersen et al (2012). A positive semidefinite band matrix can be decomposed into a sum of positive semidefinite matrices, as illustrated in Figure 2.…”

Section: Robust Stability Analysismentioning

confidence: 99%

Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems

Pakazad

Andersen

Hansson

et al. 2013

IFAC Proceedings Volumes

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Abstract:We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected uncertain systems. To facilitate distributed implementation of robust stability analysis of such systems, we describe two algorithms based on decomposition and simultaneous projections. The first algorithm is a nonlinear variant of Cimmino's mean projection algorithm, but by taking the structure of the constraints into account, we can obtain a faster rate of convergence. The second algorithm is devised by applying the alternating direction method of multipliers to a convex minimization reformulation of the convex feasibility problem. Numerical results are then used to show that both algorithms require far less iterations than the accelerated nonlinear Cimmino algorithm.

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IQC based robust stability verification for a networked system with communication delays

Wang

Zhou

2018

Sci. China Inf. Sci.

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In this paper, we consider robust stability analysis of a networked system with uncertain communication delays. Each of its subsystems can have different dynamics, and interconnections among its subsystems are arbitrary. It is assumed that there exists an uncertain but constant delay in each communication channel. Using the so called integral quadratic constraint (IQC) technique, a sufficient robust stability condition is derived utilizing a sparseness assumption of the interconnections, and a set of decoupled robustness conditions are further derived which depend only on parameters of each subsystem, the subsystem connection matrix (SCM) and the selected IQC multipliers. These characteristics result in an evident improvement of computational efficiency for robustness verification of the networked system with delay uncertainties, which is illustrated by some numerical results. Keywords large scale networked system, time delay, robust stability, integral quadratic constraints, linear matrix inequalities Citation Wang Z K, Zhou T. IQC based robust stability verification for a networked system with communication delays.

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Distributed robust stability analysis of interconnected uncertain systems

Cited by 14 publications

References 34 publications

On the Stability and Robust Stability of Networked Dynamic Systems

On the Stability and Robust Stability of Networked Dynamic Systems

Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems

IQC based robust stability verification for a networked system with communication delays

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