Robust stability, $\mathscr{H}_{2}$ and $\mathscr{H}_{\infty}$ guaranteed costs for discrete time-varying uncertain linear systems with constrained parameter variations

Bertolin, Ariádne L. J.; Peres, Pedro L. D.; Oliveira, Ricardo C. L. F.

doi:10.23919/acc.2019.8814458

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Lemma 1 Consider the GS − DOF control (6) and system (7). The later has H ∞ -performance bound (α) if a matrix P ∞ (ξ) ∈ R 2n×2n be in existence and a matrix G(ξ) ∈ R 2n×2n , which are symmetric positive-definite, such that, ∀k ≥ 0, the following retains, …”

Section: Dynamic Output Feedback Control Synthesize Lmismentioning

confidence: 99%

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LPV Control Synthesis for Sensor Senescence in Feedback Control System

Madhag

2021

IJEEI

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The senescence of system sensor(s) probably causing degenerate system behavior or system breakdown. Motivated by that, this work considers the synthesis of a gain scheduling control for linear parameter varying (LPV) system via linear matrix inequalities (LMIs) techniques such that sensors senescence information incorporated in the design of the controller. That is, the degradation of sensor effectiveness due to senescence is modeled by the variation of sensor measurements' noise co-variance. The sensors' senescence information is incorporated as a part of the scheduling parameters for the LPV controller. The synthesis control matrices via linear matrix inequalities have been re-structured and re-formalized in a way that they incorporate the sensors senescence information to synthesize a gain scheduling dynamic output feedback (GS − DOF) control. That is, the existing GS − DOF control design LMIs have been modified to include the noise co-variance matrix. The significant achievement is the control design conditions description of GS − DOF control in a way that ensures the desired integrated H2&H∞ performances in the presence of sensors senescence, where sensors' senescence information is incorporated as a part of the scheduling parameters for the LPV controller. In addition, two sets of controllers have been synthesized and studied. The simulation expresses the benefits of the proposed controllers, and closed loop system H∞ and H2 performances are also studied. The synthesized controller ensures the performance associate with a closed loop, the closed loop system stability, and the scheme of control is simple enough for real time implementations.

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Section: Dynamic Output Feedback Control Synthesize Lmismentioning

confidence: 99%

“…In the same manner, the multiobjective (i.e., mixed H 2 &H ∞ ) LPV control synthesis trend has been considered also, for example, Refs. [6][7][8]. The point against all the above literature is that they consider the output measurement may (or not) be affected by a known and timeinvariant statistical characteristics noise.…”

Section: Introductionmentioning

confidence: 99%

LPV Control Synthesis for Sensor Senescence in Feedback Control System

Madhag

2021

IJEEI

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Gain-scheduled ℋ∞ controller synthesis for LPV systems subject to multiplicative noise

2020

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Robust Control Based on Observed States Designed by Means of Linear Matrix Inequalities for Grid-Connected Converters

Koch

Osório²,

Oliveira

et al. 2023

Energies

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This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results.

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Robust stability, $\mathscr{H}_{2}$ and $\mathscr{H}_{\infty}$ guaranteed costs for discrete time-varying uncertain linear systems with constrained parameter variations

Cited by 3 publications

References 29 publications

LPV Control Synthesis for Sensor Senescence in Feedback Control System

LPV Control Synthesis for Sensor Senescence in Feedback Control System

Gain-scheduled ℋ∞ controller synthesis for LPV systems subject to multiplicative noise

Robust Control Based on Observed States Designed by Means of Linear Matrix Inequalities for Grid-Connected Converters

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