Stability analysis and control of a class of LPV systems with piecewise constant parameters

Briat, Corentin

doi:10.1016/j.sysconle.2015.05.002

Cited by 48 publications

(65 citation statements)

References 44 publications

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“…7 ; where the time-varying parameter ρ(t) takes values in P = [0,ρ],ρ > 0. It is known [36] that this system is quadratically stable if and only ifρ ≤ 3.828 but it is was later proven in the context of piecewise constant parameters [24] that this bound can be improved provided that discontinuities do not occur too often. We now apply the conditions of Theorem 2 and Theorem 3 in order to characterize the impact of parameter variations between discontinuities.…”

Section: Examplementioning

confidence: 99%

“…Finally, they can also be used to approximate parameter trajectories that exhibit intermittent very fast, yet differentiable, variations. Despite being similar to the case of piecewise constant parameters, the fact that the parameters are time-varying between discontinuities leads to additional difficulties which prevent from straightforwardly extending the approach developed in [24]. To overcome this, we propose a different, more general, approach based on hybrid systems theory [28].…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of LPV systems with piecewise differentiable parameters

Briat

Khammash

2017

IFAC-PapersOnLine

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Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of hybrid systems. The underlying idea is to reformulate the considered LPV system as an equivalent hybrid system that will incorporate, through a suitable state augmentation, information on both the dynamics of the state of the system and the considered class of parameter trajectories. Then, using a result pertaining on the stability of hybrid systems, two stability conditions are established and shown to naturally generalize and unify the wellknown quadratic and robust stability criteria together. The obtained conditions being infinite-dimensional, a relaxation approach based on sum of squares programming is used in order to obtain tractable finite-dimensional conditions. The approach is finally illustrated on two examples from the literature. * Corentin Briat and Mustafa Khammash are with the

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Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability analysis of LPV systems with piecewise differentiable parameters

Briat

Khammash

2017

IFAC-PapersOnLine

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“…The objective of the paper is to extend the framework of [18] to the case where the jumps in the parameter trajectories now occur spontaneously and in a Poissonian way (i.e. the time between two successive jumps is exponentially distributed).…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and State-Feedback Control of LPV Systems With Piecewise Constant Parameters Subject to Spontaneous Poissonian Jumps

Briat

2018

IEEE Control Syst. Lett.

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LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps are a class of systems that does not seem to have been thoroughly considered in the literature. We partially fill this gap here by providing sufficient stability and performance analysis conditions stated in terms of infinite-dimensional LMI problems that can be solved using sum of squares programming. A particularity of the obtained conditions lies in the presence of an integral term leading to some technical difficulties when attempting to obtain convex conditions for the design of a gain-scheduled statefeedback controller. This difficulty is circumvented by relying on a recent result for time-delay systems analysis and an equivalent integral-free LMI condition is obtained. The approach is illustrated through several examples. * Corentin Briat is an independent researcher. email: corentin@briat.info; url: www.briat.info arXiv:1801.03464v2 [math.OC]

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“…For example, the control for the linear parameter-varying systems with piecewise constant parameters, the signal transmission system, and the fluid power electrohydraulic actuator system have been extensively investigated; see examples including [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Adaptive PID and Model Reference Adaptive Control Switch Controller for Nonlinear Hydraulic Actuator

Zuo

Liu

Wang

et al. 2017

Mathematical Problems in Engineering

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Nonlinear systems are modeled as piecewise linear systems at multiple operating points, where the operating points are modeled as switches between constituent linearized systems. In this paper, adaptive piecewise linear switch controller is proposed for improving the response time and tracking performance of the hydraulic actuator control system, which is essentially piecewise linear. The controller composed of PID and Model Reference Adaptive Control (MRAC) adaptively chooses the proportion of these two components and makes the designed system have faster response time at the transient phase and better tracking performance, simultaneously. Then, their stability and tracking performance are analyzed and evaluated by the hydraulic actuator control system, the hydraulic actuator is controlled by the electrohydraulic system, and its model is built, which has piecewise linear characteristic. Then the controller results are compared between PID and MRAC and the switch controller designed in this paper is applied to the hydraulic actuator; it is obvious that adaptive switch controller has better effects both on response time and on tracking performance.

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Stability analysis and control of a class of LPV systems with piecewise constant parameters

Cited by 48 publications

References 44 publications

Stability analysis of LPV systems with piecewise differentiable parameters

Stability analysis of LPV systems with piecewise differentiable parameters

Stability Analysis and State-Feedback Control of LPV Systems With Piecewise Constant Parameters Subject to Spontaneous Poissonian Jumps

Adaptive PID and Model Reference Adaptive Control Switch Controller for Nonlinear Hydraulic Actuator

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