Nonlinear impulsive systems: 2D stability analysis approach

Ríos, Héctor; Hetel, Laurentiu; Efimov, Denis

doi:10.1016/j.automatica.2017.01.010

Cited by 16 publications

(7 citation statements)

References 23 publications

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“…Passivation-based arguments are also used in Forni et al [2011]. Stability analysis for nonlinear systems involving some resetting action at fixed time instants was also provided in Rios et al [2017].…”

Section: An Overview Of Recent Reset Systems Resultsmentioning

confidence: 99%

Analysis and Synthesis of Reset Control Systems

Prieur

Queinnec²,

Tarbouriech³

et al. 2018

FNT in Systems and Control

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This survey paper overviews a large core of research results produced by the authors in the past decade about reset controllers for linear and nonlinear plants. The corresponding feedback laws generalize classical dynamic controllers because of the interplay of mixed continuous/discrete dynamics. The obtained closed-loop system falls then within the category of hybrid dynamical systems, with the specific feature that the hybrid nature arises from the nature of the controller, rather than the nature of the plant, which is purely continuous-time. Due to this fact, the presented results focus on performance and stability notions that prioritize continuous-time evolution as compared to the discrete-time one. Dwell-time logics are indeed enforced on solutions, to ensure that the continuous evolution of solutions is complete (no Zeno solutions occur). After presenting a historical motivation and an overview of the results on this topic in Part I, several results on stability and performance analysis and on control design for general linear continuous-time plants are developed in Part II. These results are developed by exploiting the well established formalism for nonlinear hybrid dynamical systems introduced by Andy Teel and co-authors around 2004. With this formalism, by ensuring sufficient regularity of the reset controller dynamics, we ensure robustness of stability with respect to small disturbances and uncertainties together with suitable continuity of solutions, generally regarded as well-posedness of the hybrid closed loop. Throughout Part II, we provide several simulation studies showing that reset control strategies may allow to attain better performance with respect to the optimal ones obtained by classical continuous-time controllers. Finally, In Part III we focus on planar systems, that is reset closed loops involving a one dimensional linear plant and a one dimensional reset controller. For this simple interconnection interesting stability conditions can be drawn and relevant extensions addressing the reference tracking problem are introduced, illustrating them on a few relevant 2 case studies emerging in the automotive field.

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Section: An Overview Of Recent Reset Systems Resultsmentioning

confidence: 99%

Analysis and Synthesis of Reset Control Systems

Prieur

Queinnec²,

Tarbouriech³

et al. 2018

FNT in Systems and Control

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“…In the present section some definitions and results for the stability of impulsive systems, in the framework of 2D systems, are introduced (see [26] and [27]).…”

Section: Stability Analysis For Impulsive Systemsmentioning

confidence: 99%

“…Therefore, the matrix Ξ 2 (Θ) can be upper estimated as Ξ 2 (Θ) ≤ Ξ 3 (Θ), where Ξ 3 (Θ), is defined by Ξ 3 (Θ) =   Ψ 1 (Θ)P (3)P (4) − Therefore, the LMI (27) is obtained when all the elements of Ξ 3 (Θ) are merged, and one conclude that if the set of LMIs (27) and (29) is feasible then Υ 1 (Θ) ≤ 0.…”

Section: Proof Of Propositionmentioning

confidence: 99%

“…[28] and [31]), for stability of impulsive systems is used for designing a robust output-feedback control for linear sampled-data systems. Such an approach, proposed in [26] and [27], provides a stability analysis based on linear matrix inequalities (LMIs) for linear impulsive dynamical systems. Then, it is possible to show that the sampled-data control problem based on state estimation may turn into one of finding conditions for the exponential stability of impulsive systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust output-feedback control for uncertain linear sampled-data systems: A 2D impulsive system approach

Ríos

Hetel

Efimov

2019

Nonlinear Analysis: Hybrid Systems

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This paper deals with the sampled-data control problem based on state estimation for uncertain linear sampled-data systems. It is possible to show that the sampled-data control problem based on state estimation may be related with the conditions for the exponential stability of impulsive systems. Thus, a vector Lyapunov function-based approach, derived by means of a 2D time domain equivalence, is used for obtaining stability conditions of an impulsive system, and then, a solution to the observer-based control design problem is derived and expressed in terms of LMIs. Some examples illustrate the feasibility of the proposed approach.

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“…In this context, the available studies are almost exclusively focused on stability analysis and stabilization methods. The current literature provides some results about stability analysis for nonlinear impulsive systems based on discontinuous Lyapunov functions [6], switched Lyapunov functions and LMIs [7], average impulse interval [8], 2D time domain representation and vector Lyapunov functions [9]. The design of stabilizing feedbacks is investigated in [7] and optimal control problems for nonlinear impulsive systems are discussed in [3].…”

Section: Introductionmentioning

confidence: 99%