Sufficient LMI conditions for output feedback control problems

Crusius, C.A.R.; Trofino, Alexandre

doi:10.1109/9.763227

Cited by 458 publications

(263 citation statements)

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“…There has been extensive research on finding appropriate related convex problem formulations via a change of variables [25]. Among others, one possible variable change leads to the W -Problem [26]. Applying this variable transformation to equations (III.11) leads to the proposed LMI optimization problem stated in Theorem 3.4.…”

Section: Theorem 34mentioning

confidence: 99%

On power sharing and stability in autonomous inverter-based microgrids

Schiffer

Anta

Trung

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-We consider the problem of voltage and frequency stability for an autonomous inverter-based microgrid. An LMIbased decentralized feedback control design is derived that stabilizes the system under the consideration of droop-like controllers aiming to achieve power sharing among the different generation units. We provide a design procedure that accounts for uncertainties in line impedances and loads while guaranteeing zero steady-state frequency deviation.

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Section: Theorem 34mentioning

confidence: 99%

On power sharing and stability in autonomous inverter-based microgrids

Schiffer

Anta

Trung

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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“…Inequality (36) has the same form as static output feedback stabilization: several numerical methods have been proposed in literature for the solution of this problem [27], [28], [29], [30], [31]. Next, the iterative method proposed in [29] is elaborated for the adaptive mixing control architecture in order to solve the synthesis problem.…”

Section: Algorithm 2 Analysis Problemmentioning

confidence: 99%

Stability margins in adaptive mixing control via a Lyapunov-based switching criterion

Baldi¹,

Ιωάννου²

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-This paper proposes a Lyapunov-based switching logic within the framework of adaptive mixing control (AMC), where a weighted combination of a family of candidate controllers can be inserted in the loop to regulate the output of an uncertain plant. The proposed AMC scheme employs a bank of parallel estimators, or multiple estimators, together with a switching logic that orchestrates which estimate should be evaluated by the mixer. The switching logic is driven by input/output data and uses Lyapunov-based criteria to assess the best estimate among the bank of parallel estimates. The resulting scheme guarantees convergence of the switching signal in finite time to a controller that satisfies a Lyapunov inequality implying a prescribed stability margin. The problem of convergence to the desired controller is addressed both analytically and numerically. In contrast, most classes of continuous tuning adaptive control or switching adaptive control schemes do not guarantee that after the switching stops or the adaptation is switched off the resulting closed loop linear time-invariant (LTI) system is stable, unless there is sufficient plant excitation that guarantees convergence to the desired fixed parameter controller. The proposed scheme guarantees that if the desired controller is switched on, it will never be switched off thereafter. Furthermore, simulations demonstrate that while alternative adaptation methods can converge to an LTI unstable feedback loop, the proposed scheme consistently converges to the desired controller.

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“…Therefore, (38) can be used for robust controller design either directly -using appropriate BMI solver (Henrion et al, 2005) or using some convexifying approach, (for discrete-time case see e.g. (Crusius & Trofino, 1999;deOliveira et al, 1999)). We have relatively good experience with the following simple convexified LMI procedure for static output feedback discrete-time controller design, which is directly applicable for discretetime PID controller design problem formulated by (26), (27b), (28b).…”

Section: Corollary 31mentioning

confidence: 99%