References of "IEEE Transactions on Automatic Control"
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See detailA differential Lyapunov framework for contraction analysis
Forni, Fulvio ULg; Sepulchre, Rodolphe ULg

in IEEE Transactions on Automatic Control (2014), 59(3), 614-628

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to ... [more ▼]

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. [less ▲]

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See detailGlobal analysis of a continuum model for monotone pulse-coupled oscillators
Mauroy, Alexandre ULg; Sepulchre, Rodolphe ULg

in IEEE Transactions on Automatic Control (2013), 58(5), 1154-1166

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupledmodels, the stability results ... [more ▼]

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupledmodels, the stability results obtained in the continuum limit are global. For the nonlinear transport equation governing the evolution of the oscillators, we propose (under technical assumptions) a global Lyapunov function which is induced by a total variation distance between quantile densities. The monotone time evolution of the Lyapunov function completely characterizes the dichotomic behavior of the oscillators: either the oscillators converge in finite time to a synchronous state or they asymptotically converge to an asynchronous state uniformly spread on the circle. The results of the present paper apply to popular phase oscillators models (e.g., the well-known leaky integrate-and-fire model) and show a strong parallel between the analysis of finite and infinite populations. In addition, they provide a novel approach for the (global) analysis of pulse-coupled oscillators. © 2012 IEEE. [less ▲]

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See detailFollow the bouncing ball: global results on tracking and state estimation with impacts
Forni, Fulvio ULg; Teel, Andrew; Zaccarian, Luca

in IEEE Transactions on Automatic Control (2013)

In this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories ... [more ▼]

In this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations. [less ▲]

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See detailLyapunov-based sufficient conditions for exponential stability in hybrid systems
Teel, Andrew; Forni, Fulvio ULg; Zaccarian, Luca

in IEEE Transactions on Automatic Control (2013)

Lyapunov-based sufficient conditions for exponential stability in hybrid systems are presented. The focus is on converting non-strict Lyapunov conditions, having certain observability properties, into ... [more ▼]

Lyapunov-based sufficient conditions for exponential stability in hybrid systems are presented. The focus is on converting non-strict Lyapunov conditions, having certain observability properties, into strict Lyapunov conditions for exponential stability. Both local and global results are considered. The utility of the results is illustrated through an example. [less ▲]

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See detailCoordinated motion design on Lie groups
Sarlette, Alain ULg; Bonnabel, Silvere; Sepulchre, Rodolphe ULg

in IEEE Transactions on Automatic Control (2010), 55(5), 1047-1058

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it ... [more ▼]

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3) , SE(2) and SE(3). [less ▲]

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See detailA Family of Global Stabilizers for Quasi-Optimal Control of Planar Linear Saturated Systems
Forni, Fulvio ULg; Galeani, Sergio; Zaccarian, Luca

in IEEE Transactions on Automatic Control (2010), 55(5), 1175-1180

We propose a family of nonlinear state feedback global stabilizers for all planar linear systems which are globally stabilizable by bounded inputs (namely, all non exponentially unstable linear systems ... [more ▼]

We propose a family of nonlinear state feedback global stabilizers for all planar linear systems which are globally stabilizable by bounded inputs (namely, all non exponentially unstable linear systems). This family is parametrized by a nonlinear function whose selection can yield quasi time-optimal responses, where the "quasi" is required to achieve local exponential stability of the closed loop. The arising trajectories are quasi-time-optimal for arbitrarily large initial conditions; so, we expect the very simple proposed nonlinear control law to be very useful for embedded control applications with strong computational constraints. [less ▲]

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See detailRobust and Adaptive Observer-Based Partial Stabilization for a Class of Nonlinear Systems
Efimov, Denis ULg; Fradkov, Alexander

in IEEE Transactions on Automatic Control (2009), 54(7),

The problem of adaptive stabilization with respect to a set for a class of nonlinear sys- tems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case ... [more ▼]

The problem of adaptive stabilization with respect to a set for a class of nonlinear sys- tems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case of noisy measurements is proposed. The efficiency of proposed solution is demonstrated via example of swinging a pendulum with unknown parameters. [less ▲]

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See detailStabilization of Planar Collective Motion With Limited Communication
Sepulchre, Rodolphe ULg; Paley, Derek; Leonard, Naomi E.

in IEEE Transactions on Automatic Control (2008), 53(3), 706-719

This paper proposes a designmethodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel ... [more ▼]

This paper proposes a designmethodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or timevarying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. [less ▲]

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See detailStabilization of planar collective motion: All-to-all communication
Sepulchre, Rodolphe ULg; Paley, Derek; Leonard, Naomi Ehrich

in IEEE Transactions on Automatic Control (2007), 52(5), 811-824

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria ... [more ▼]

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. [less ▲]

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See detailAnalysis of interconnected oscillators by dissipativity theory
Stan, G. B.; Sepulchre, Rodolphe ULg

in IEEE Transactions on Automatic Control (2007), 52(2), 256-270

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a ... [more ▼]

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators. [less ▲]

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See detailTrading the Stability of Finite Zeros for Global Stabilization of Nonlinear Cascade Systems
Sepulchre, Rodolphe ULg; Arcak, Murat; Teel, Andrew R.

in IEEE Transactions on Automatic Control (2002), 47(3), 521-525

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the ... [more ▼]

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions. [less ▲]

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See detailRobust global state feedback stabilization of cement mills
Grognard, F.; Jadot, F.; Magni, L. et al

in IEEE Transactions on Automatic Control (2001), 46(4), 618-623

Plugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust ... [more ▼]

Plugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust controller can be designed in order to fully prevent the mill from plugging [less ▲]

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See detailSlow Peaking and Low-Gain Designs for Global Stabilization of Nonlinear Systems
Sepulchre, Rodolphe ULg

in IEEE Transactions on Automatic Control (2000), 45(3), 453-461

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See detailLyapunov functions for stable cascades and applications to global stabilization
Mazenc, F.; Sepulchre, Rodolphe ULg; Jankovic, M.

in IEEE Transactions on Automatic Control (1999), 44(9), 1795-1800

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems one of which is stable rather than asymptotically stable. A new a cross term construction in the Lyapunov ... [more ▼]

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems one of which is stable rather than asymptotically stable. A new a cross term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boudedness condition. This method is instrumental in the global stabilization of feedforward systems and new stabilization results are derived from the generalized construction. [less ▲]

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See detailShape signifiers for throttle control of a low-order compressor model
Sepulchre, Rodolphe ULg; Kokotovic, Petar

in IEEE Transactions on Automatic Control (1998), 43(11), 1643-1648

Rotating stall and surge, two instability mechanisms limiting the performance of aeroengines compressors, are studied on the third-order Moore–Greitzer model. The skewness of the compressor characteristic ... [more ▼]

Rotating stall and surge, two instability mechanisms limiting the performance of aeroengines compressors, are studied on the third-order Moore–Greitzer model. The skewness of the compressor characteristic, a single parameter shape signifier, is shown to determine the key qualitative properties of feedback control. [less ▲]

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See detailConstructive Lyapunov stabilization of nonlinear cascade systems
Jankovic, M.; Sepulchre, Rodolphe ULg; Kokotovic, Petar V.

in IEEE Transactions on Automatic Control (1996), 41(12), 1723-1735

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