Generalized Feedback Homogenization and Stabilization of Linear MIMO Systems

Zimenk, Konstantin; Polyako, Andrey; Efimo, Denis; Perruquett, Wilfrid

doi:10.23919/ecc.2018.8550195

Cited by 6 publications

(6 citation statements)

References 22 publications

(29 reference statements)

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“…This manuscript describes an implicit homogeneous con-trol (IHC) (see [7], [9] and [13]) to regulate the linearized approximation of nonlinear mechanical systems. The control design is essentially based on the so-called canonical homogeneous norm [9], which defines an implicit Lyapunov function that leads to the obtention of the control gains design [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Practical Realization of Implicit Homogeneous Controllers for Linearized Systems

Cruz-Ortiz

Ballesteros

Polyakov

et al. 2022

IEEE Trans. Ind. Electron.

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This paper deals with the practical implementation of implicit homogeneous controllers (IHCs) for linearized mechanical systems. The control design includes the methodology to get gains of the IHC based on the linearized approximation of the system. If the approximation error enforced by the linearization is vanishing with the state, locally measurable and bounded, the IHC can lead the state to the origin in finite-time. This IHC control allows accelerating the convergence rate of the states. A semi-explicit algorithm is provided to exert the digital implementation of the controller. The application of the bisection method estimates the controller gain ensuring the finite-time convergence of the state to the origin. A complementary analysis provides a simplified algorithm with a reduced number of computation stages but equally efficient gain estimation. The proposed IHC is applied to a rotary inverted pendulum QUBE ™ Servo 2 platform of Quanser ® . The obtained results for the state convergence are compared with other classical feedback controllers to validate the effectiveness of the proposed scheme. The comparative analysis of the state convergence provides evidence of the faster convergence for the state trajectory to a zone centered on the origin with a smaller hypervolume than the one gotten with the classical controllers.

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Section: Introductionmentioning

confidence: 99%

Practical Realization of Implicit Homogeneous Controllers for Linearized Systems

Cruz-Ortiz

Ballesteros

Polyakov

et al. 2022

IEEE Trans. Ind. Electron.

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“…There are a lot of topics for future research. For example, the presented results can be extended for linear MIMO systems using generalized homogenising stabilization algorithm presented in [30]. Other directions are relaxation of restrictions, extension to output control case, study of transient performances, etc.…”

Section: Resultsmentioning

confidence: 99%

Independent of delay stabilization using implicit Lyapunov function method

et al. 2019

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Nonlinear implicit Lyapunov function based control algorithms with delay in control and/or measurement channel are presented. The proposed control algorithms provide global asymptotic stability for all delays less than a certain threshold value and global asymptotic stability with respect to a compact set containing the origin for any delay over the threshold value. The algorithms are also applicable for the fast-varying delay and sampled-data cases. The theoretical results are supported by numerical simulations and comparison.

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“…Theorem 1 [8], [10] Suppose there exist a positive definite C 1 function V defined on an open neighborhood of the origin D ⊂ R n and real numbers C > 0 and σ ≥ 0, such that the following condition is true for the system (1)…”

Section: Preliminaries a Stability Notionsmentioning

confidence: 99%

“…In comparison with the conference version [1], in addition to detailed proofs, the presented results allow to derive necessary conditions of generalized homogenizability and homogeneous stabilizability of linear MIMO systems. Moreover, it is shown that if a system is homogeneously stabilizable of nonzero degree then it is homogeneously stabilizable with any degree.…”

Section: Introductionmentioning

confidence: 99%

Robust Feedback Stabilization of Linear MIMO Systems Using Generalized Homogenization

Zimenko

Polyakov

Efimov

et al. 2020

IEEE Trans. Automat. Contr.

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A robust nonlinear control is designed for stabilizing linear MIMO systems. The presented control law homogenizes a linear system (without its transformation to a canonical form) with a specified degree and stabilizes it in a finite time (or with a fixed-time attraction to any compact set containing the origin) if the degree of homogeneity is negative (positive). The tuning procedure is formalized in LMI form. Performance of the approach is illustrated by numerical and experimental examples.

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Generalized Feedback Homogenization and Stabilization of Linear MIMO Systems

Cited by 6 publications

References 22 publications

Practical Realization of Implicit Homogeneous Controllers for Linearized Systems

Practical Realization of Implicit Homogeneous Controllers for Linearized Systems

Independent of delay stabilization using implicit Lyapunov function method

Robust Feedback Stabilization of Linear MIMO Systems Using Generalized Homogenization

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