A frequency domain condition for stability of interconnected MIMO systems

Gattami, Ather; Murray, Richard M.

doi:10.23919/acc.2004.1384491

Cited by 28 publications

(45 citation statements)

References 7 publications

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“…The network structures and decomposition techniques we consider here are similar to previous works on synchronization problems [15,13], consensus problems [14], vehicle formations [5], Internet congestion control [4,9,10], and other network problems with symmetry such as [1,6]. One characteristic for all these applications is that it has been possible to derive analysis and design results that are completely decentralized in the sense that conditions for stability and performance can be obtained using only local information and possibly some spectral characteristic of the interconnection matrix.…”

Section: Introductionmentioning

confidence: 99%

A Popov criterion for networked systems

Jönsson

Kao

Fujioka

2007

Systems & Control Letters

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We consider robustness analysis of heterogeneous and homogeneous networked systems based on integral quadratic constraints (IQCs). First, we show how the analysis decomposes into lower dimensional problems if the interconnection structure is exploited. This generally leads to a significant reduction of the computational complexity. Secondly, by considering a set of IQCs that characterizes the eigenvalues of the interconnection matrices of symmetrically networked systems, we derive a Popov-like criterion for such systems. In particular, when the nodes of the networked system are single-input-single-output linear time-invariant operators, the criterion can be illustrated using a generalized Popov plot. In such cases, the Popov criterion is also a necessary condition in the sense that if the criterion is violated then a destabilizing network with the specified eigenvalue distribution can be constructed.

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Section: Introductionmentioning

confidence: 99%

A Popov criterion for networked systems

Jönsson

Kao

Fujioka

2007

Systems & Control Letters

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“…In the networked MAS, consensus means to reach an agreement regarding a certain quantity of interest that depends on the state of of dynamical agents. Consensus algorithm with graph theory has been studied as a control problem of MAS in [5]- [8]. In [5] and [6], proposes a new control law to which consensus algorithm [7] is enhanced.…”

Section: Introductionmentioning

confidence: 99%

“…Consensus algorithm with graph theory has been studied as a control problem of MAS in [5]- [8]. In [5] and [6], proposes a new control law to which consensus algorithm [7] is enhanced. It was shown in [5] that stability of MAS could be checked graphically using Nyquist-like criterion.…”

Section: Introductionmentioning

confidence: 99%

“…In [5] and [6], proposes a new control law to which consensus algorithm [7] is enhanced. It was shown in [5] that stability of MAS could be checked graphically using Nyquist-like criterion. Depending on the agent system, it is dif cult to design controllers using Nyquist-like criterion.…”

Section: Introductionmentioning

confidence: 99%

“…Also, [6] derive condition of stability of MAS using Lyapunov stability theorem under assumed unidirectional network (balanced graph) where an agent is second-order system. So the MAS is much less common than [5]. Therefore we consider that each agent is MIMO linear system and propose the condition of stability using Lyapunov stability theorem.…”

Section: Introductionmentioning

confidence: 99%

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Consensus control of observer-based multi-agent system with Communication Delay

Namerikawa

Yoshioka

2008

2008 SICE Annual Conference

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This paper proposes an observer-based consensus control strategy for multi-agent system (MAS) with communication time delay. The condition of stability for MIMO agents is derived by Lyapunov theorem. It gives systematic design procedure under assumed unidirectional network. Furthermore, new consensus control law using observers is proposed for the networked MAS with communication delays. Experimental results show effectiveness of our proposed output consensus approaches.

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Consensus of positive real systems cascaded with a single integrator

Lashhab

Moore

et al. 2013

Intl J Robust & Nonlinear

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SUMMARYWe study output consensus in a network of interconnected non-identical positive real systems cascaded with a single integrator. Assuming undirected, diffusive interconnections, sufficient conditions are provided to ensure output consensus for two cases: (i) the individual systems are weakly strictly positive real systems cascaded with a single integrator, and (ii) the individual systems are positive real systems cascaded with a single integrator. We illustrate our results with the example of a load frequency control network of synchronous generators.

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A frequency domain condition for stability of interconnected MIMO systems

Cited by 28 publications

References 7 publications

A Popov criterion for networked systems

A Popov criterion for networked systems

Consensus control of observer-based multi-agent system with Communication Delay

Consensus of positive real systems cascaded with a single integrator

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