On the practical stability of control processes governed by implicit differential equations: The invariant ellipsoid based approach

Azhmyakov, Vadim; Poznyak, Alexander S.; Juárez, R.

doi:10.1016/j.jfranklin.2013.04.016

Cited by 19 publications

(30 citation statements)

References 24 publications

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“…Notice that (5) is not restrictive and comprises a large class of unknown nonlinear functions [17,18]. By defining the auxiliary function…”

Section: Basic Assumptionsmentioning

confidence: 99%

“…This paper deals with the quantization problem by applying the invariant ellipsoid method [11][12][13][14][15][16]. This allows us to design dynamic feedback control laws for a class of nonlinear systems satisfying a quasi-Lipschitz condition [17,18]. In fact, the class of systems is fairly large, as it includes systems with hard or even discontinuous non linearities.…”

Section: Introductionmentioning

confidence: 99%

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Robust feedback design for stabilization of nonlinear systems with sampled-data and quantized output: Atractive ellipsoid method

Poznyak

2015

Autom Remote Control

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For a wide class of nonlinear systems, containing internal uncertainties as well as external bounded perturbations, the technique for robust feedback designing is suggested. The class of stabilizing dynamic feedbacks with a given linear structure is characterized by the corresponding BMI's, which is shown to be reduced to the system of LMI's. The optimal parameters of the feedback controllers realize the matrix solution to the conditional optimization problems under a set of specific linear matrix constraints. This optimization problem is solved by the standard MATLAB packages. Numerical examples illustrate the workability of the suggested approach.

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“…Notice that (5) is not restrictive and comprises a large class of unknown nonlinear functions [17,18]. By defining the auxiliary function…”

Section: Basic Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust feedback design for stabilization of nonlinear systems with sampled-data and quantized output: Atractive ellipsoid method

Poznyak

2015

Autom Remote Control

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“…Notice that Equation (4) is not restrictive and comprises a large class of unknown nonlinear functions (Azhmyakov, Poznyak, & Gonzalez, 2013;Azhmyakov, Poznyak, & Juárez, 2013). By defining the auxiliary function ω x (t) := υ x (t) + f(t, x(t)) − Ax(t), we can rewrite Equation (1) in the quasi-linear formaṫ…”

Section: Assumption 21mentioning

confidence: 99%

“…Email: castanos@ieee.org attractive ellipsoid method (Davila & Poznyak, 2011;Glover & Schweppe, 1971;Kurzhanski & Varaiya, 2006;Polyak, Nazin, Durieu, & Walter, 2004;Polyak & Topunov, 2008). This allows us to design dynamic feedback control laws for a class of nonlinear systems satisfying a quasiLipschitz condition (Azhmyakov, Poznyak, & Gonzalez, 2013;Azhmyakov, Poznyak, & Juárez, 2013). The class of systems is fairly large, as it includes systems with hard or even discontinuous nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Quantised and sampled output feedback for nonlinear systems

Mera

Castaños

Poznyak

2014

International Journal of Control

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In this paper we consider the analysis and design of an output feedback controller for a perturbed nonlinear system in which the output is sampled and quantised. Using the attractive ellipsoid method, which is based on Lyapunov analysis techniques, together with the relaxation of a nonlinear optimisation problem, sufficient conditions for the design of a robust control law are obtained. Since the original conditions result in nonlinear matrix inequalities, a numerical algorithm to obtain the solution is presented. The obtained control ensures that the trajectories of the closed-loop system will converge to a minimal (in a sense to be made specific) ellipsoidal region. Finally, numerical examples are presented in order to illustrate the applicability of the proposed design method.

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“…Other than autonomous ship deck landing of UAVs, invariant ellipsoid method is also applied in other situations such as spacecraft stabilization [21] and sliding mode control [22]. Extensions to this method are developed in [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Autonomous ship deck landing of a quadrotor using invariant ellipsoid method

Tan

Wang

Paw

et al. 2016

IEEE Trans. Aerosp. Electron. Syst.

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This paper proposes an invariant ellipsoid-based method for the controller design and gain synthesis of a low-cost quadrotor autonomous ship deck landing system subjected to wind disturbance and measurement noise. This method optimizes the quadrotor performance, hence achieving soft landing. A complete control architecture for the quadrotor is also presented. Simulations are performed using a realistic ship deck model in the presence of measurement noise and wind disturbance with a quadrotor. has been with the School of Electrical and Electronic Engineering at Nanyang Technological University, Singapore, where he is currently an associate professor. His research interest includes multiagent systems, vision-based control systems, robust and reliable control, path planning and trajectory generation, and flight control systems. Yew Chai Paw received the B.Eng. and M.Eng. degrees in mechanical and aerospace engineering from Nanyang Technology University, Singapore, in 2000 and 2005, respectively. He received the Ph.D. degree in aerospace engineering in 2009 from University of Minnesota, MN. He is currently a principal member of technical staff in DSO National Laboratories, Singapore. His research interests include UAV system engineering and flight dynamics modeling. Fang Liao received her B.E. and M.E. degrees in control and navigation, both from

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On the practical stability of control processes governed by implicit differential equations: The invariant ellipsoid based approach

Cited by 19 publications

References 24 publications

Robust feedback design for stabilization of nonlinear systems with sampled-data and quantized output: Atractive ellipsoid method

Robust feedback design for stabilization of nonlinear systems with sampled-data and quantized output: Atractive ellipsoid method

Quantised and sampled output feedback for nonlinear systems

Autonomous ship deck landing of a quadrotor using invariant ellipsoid method

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