Estimating the stability region of singular perturbation power systems with saturation nonlinearities: an linear matrix inequality-based method

SUMMARYThis paper proposes a linear matrix inequality based method for the estimation of domain of attraction for a class of discrete‐time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete‐time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. Numerical examples illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

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“…In view of (8), (9), and the RARs in (6), (10), and (11), we can recast the conditions V .x, / > 0 and V .x, / < 0 as follows:…”

Section: Towards a Convex Characterizationmentioning

confidence: 99%

Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems

Coutinho

Souza

2012

Intl J Robust & Nonlinear

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“…Actuator saturation is an ubiquitous phenomenon for physical systems, which may cause the deterioration of system performance. For saturated systems, many valuable results have been obtained . In the recent years, many design schemes for saturated normal systems were improved and utilized to saturated SPSs, and a lot of outstanding results have been achieved .…”

Section: Introductionmentioning

confidence: 99%

Observer‐based event‐triggered control for singularly perturbed systems with saturating actuator

Yan

Yang

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper investigates an observer‐based event‐triggered control problem of singularly perturbed systems with saturating actuator. A strategy that consists of an observer‐based controller (OBC) and an event‐triggered mechanism (ETM) is considered. Firstly, sufficient conditions, which guarantee that the saturated SPSs are asymptotically stable excluding Zeno phenomenon, are derived via constructing an ε‐dependent Lyapunov‐Krasovskii functional. Then, the OBC and ETM are designed simultaneously based on the aforementioned criteria. Furthermore, an estimate of the basin of attraction and an ε‐bound are given by solving an optimization problem in the form of LMIs. Finally, an electric circuit system and a numerical example are presented to demonstrate the merits of the obtained method.

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“…A controller is firstly designed without the consideration of actuator saturation and then designed as an antiwindup compensator to weaken the effect of the saturation . Recently, some researchers have focused on SPSs subject to actuator saturation . However, there are a few results on SPSSs subject to actuator saturation .…”

Section: Introductionmentioning

confidence: 99%

Disturbance rejection of singularly perturbed switched systems subject to actuator saturation

Wang

Zhou

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper addresses the disturbance rejection problem for singularly perturbed switched systems subject to actuator saturation. We focus our attention on the synthesis of feedback control laws to achieve disturbance rejection for the systems. By using the average dwell‐time approach together with the piecewise Lyapunov function technique, sufficient conditions for the existence of a controller are derived in terms of LMIs, which are independent of the singular perturbation parameter ε. Some convex optimization problems are formulated to get a larger estimate of the basin of attraction and a better disturbance rejection ability. The state‐feedback controller depends on the singular perturbation parameter ε, but it is shown to be well posed for all ε∈(0,ε0]. In addition, if ε is sufficiently small, the ε‐dependent controller can be reduced to an ε‐independent one. Finally, a hydraulic servoposition system is used to show the feasibility and effectiveness of the obtained results.

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Estimating the stability region of singular perturbation power systems with saturation nonlinearities: an linear matrix inequality-based method

Cited by 31 publications

References 22 publications

Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems

Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems

Observer‐based event‐triggered control for singularly perturbed systems with saturating actuator

Disturbance rejection of singularly perturbed switched systems subject to actuator saturation

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