On Stability of Multivariate Polynomials

Rodríguez-Angeles, E.

doi:10.5772/6024

Cited by 4 publications

(6 citation statements)

References 19 publications

(29 reference statements)

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“…One notable work analysis distributed leaderless, model-independent consensus algorithms for networked Euler-Lagrange systems [25]. Most of earlier work an leader-follower multi-agent coordination approach requires each follower to have the information access to the leader [12], [28], [27]. As a result, the network implementation becomes more complicated : costly and less robust.…”

Section: Introductionmentioning

confidence: 99%

“…A simple comparative with [11] and [26], we note that the proposed contribution managed to eliminate the all-to-all coupling and consequently decrease the number of variables to manage in network. Compared with classical leader follower structure [12], [30] our contributed work benefits of the neighbor-based rule to design a decentralized leader-follower structure such as the network do not requires direct communication channels between the leader and all followers. Also, the proposed topology permits a followerfollower data exchange.…”

Section: Introductionmentioning

confidence: 99%

“…The coordination of multi-robot systems and consensus problems are related with the synchronization problem which uses a graph theory [8]. According to Rodriguez [11], based on the type of interconnections in the system, different kinds of synchronization can be defined: mutual synchronization, when all agents occur on equal term, cooperative systems case [11], and external synchronization, when one object is more powerful than the others and its motion can be considered as independent of the motion of the other objects, master-slave systems case [12]. It is noted that there have been numerous investigations in multi-agent networks with leader-follower structure [2], [3], [4], [5], [6], [7], [9], [10].…”

Section: Introductionmentioning

confidence: 99%

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Coordinated backstepping control of multiple robot system of the leader-follower structure

Bouteraa

Ghommam

Derbel

2011

Eighth International Multi-Conference on Systems, Signals &Amp; Devices

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A decentralized control law using a backstepping scheme is proposed to deal with a leader follower multiple robots structure. The coordination strategy combines the leader follower control with the decentralized control. In fact, in the proposed approach, each follower robot only needs the information exchange with its connected neighbors and does not assume the existence of direct communication channel with the leader, which mitigate the implementation cost, mainly when the cooperative robots number increases. The objective of the designed control law is to synchronize positions and velocities of multiple followers interconnected via the neighbor-based rule with respect to the leader's state. The performance of synchronization control system and the nonlinear stability are derived by Lyapunov method, and the tracking controller successfully guarantees asymptotic convergence to zero of both position tracking and synchronization errors. Simulations were performed to demonstrate the effectiveness of the proposed synchronization control approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coordinated backstepping control of multiple robot system of the leader-follower structure

Bouteraa

Ghommam

Derbel

2011

Eighth International Multi-Conference on Systems, Signals &Amp; Devices

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“…However, the used approach in [34] is classified as centralized control. Most of earlier works in leader-follower multi-agent coordination approach require each follower to have the information access to the leader [31], [32], [33]. As a result, the network implementation becomes more complicated: costly and less robust.…”

Section: Introductionmentioning

confidence: 99%

“…The coordination of multi-robot systems and consensus problems are related with the synchronization problem which uses a graph theory [26]. According to Rodriguez [27], based on the type of interconnections in the system, different kinds of synchronization can be defined: mutual synchronization, when all agents occur on equal term, cooperative systems case [27], and external synchronization, when one object is more powerful than the others and its motion can be considered as independent of the motion of the other objects, master-slave systems case [31]. It is noted that there have been numerous investigations in multi-agent networks with leader-follower structure [29], [18], [14], [25], [19], [11], [20].…”

Section: Introductionmentioning

confidence: 99%

Adaptive backstepping synchronization for networked Lagrangian systems

Bouteraa

Ghommam²,

Poisson³

2012

IJCA

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A decentralized control law using a backstepping scheme is proposed to deal with a leader follower multiple robots structure. Based on graph theory and Laplacian, the coordination strategy combines the leader follower control with the decentralized control. In fact, in the proposed approach, each follower robot only needs the information exchange with its connected neighbors and does not assume the existence of direct communication channel with the leader, which mitigate the implementation cost, mainly when the cooperative robots number increases. The objective of the designed control law is to synchronize positions and velocities of multiple followers interconnected via the neighbor-based rule with respect to the leader's state. The proposed strategy is further extended to adaptive neural network coordination.The performance of synchronization control system and the nonlinear stability are derived by Lyapunov method. Simulations were performed to demonstrate the effectiveness of the proposed synchronization control approach. General TermsSynchronization and cooperative robot control.

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Stability analysis of 2‐D discrete and continuous state‐space systems

Kanellakis

Tawfik

Agathoklis

2021

IET Control Theory & Appl

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This paper presents new stability conditions for two-dimensional (2-D) systems in statespace description. Both discrete and continuous systems are studied. These results are based on the criteria first presented by Huang, De Carlo, Strintzis, Murray, Delsarte, et al. and on the discrete Lyapunov equation with complex elements for 2-D systems. The stability properties of the Mansour matrix are also used for stability testing in state-space. Criteria for the VSHP property of 2-D polynomials are further presented using the continuous Lyapunov equation with complex elements and the stability properties of the Schwarz matrix form. The stability properties of the Schwarz matrix are also used for testing the VSHP property of 2-D polynomials in state-space. The proposed new criteria are nonconservative for the stability analysis of 2-D discrete and continuous systems and achieve the aim of reducing the original 2-D problem as much as possible to a set of 1-D stability tests. Numerical examples are given to illustrate the utility of the proposed conditions.

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On Stability of Multivariate Polynomials

Cited by 4 publications

References 19 publications

Coordinated backstepping control of multiple robot system of the leader-follower structure

Coordinated backstepping control of multiple robot system of the leader-follower structure

Adaptive backstepping synchronization for networked Lagrangian systems

Stability analysis of 2‐D discrete and continuous state‐space systems

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