On constrained stabilization of discrete-time linear systems

Αθανασόπουλος, Νικόλαος; Doban, Alina I.; Lazăr, Mircea

doi:10.1109/med.2013.6608819

Cited by 6 publications

(8 citation statements)

References 23 publications

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“…Therefore, parametric uncertainty should be taken into account by the control design. Parametric uncertainty can be tackled either via a robust [16,17,18,19,20,21] or via an adaptive [22,23,24,25,26,27] control approach. Using an averaged model, in [16] a robust linear quadratic regulation (LQR) problem is formulated via LMIs, while in [17,18,19] the minimization of the H 2 or H ∞ norms is carried out so as to assure a guaranteed region of stability.…”

Section: Switched Dynamics Parametric Uncertainty and Related Workmentioning

confidence: 99%

“…Using an averaged model, in [16] a robust linear quadratic regulation (LQR) problem is formulated via LMIs, while in [17,18,19] the minimization of the H 2 or H ∞ norms is carried out so as to assure a guaranteed region of stability. Using a switched model, constrained stabilization of buck converters based on controlled contractive sets have been considered in [20], while model predictive control is considered in [21]. In most robust control approaches the uncertainty set is represented by a polytope inside which admissible values of the uncertain parameters are constrained.…”

Section: Switched Dynamics Parametric Uncertainty and Related Workmentioning

confidence: 99%

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Adaptive pulse width modulation design for power converters based on affine switched systems

Baldi

Papachristodoulou

Kosmatopoulos

2018

Nonlinear Analysis: Hybrid Systems

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In this work we propose a novel adaptive switching strategy for the design of pulse width modulation signals in power converters. Instead of an uncertain averaged model of the power converter, an uncertain switched model is considered, which can better represent the actual power converter dynamics. Uncertainties in the power converters parameters are handled via an adaptive control approach, and all circuit parameters of the switched model are assumed to be unknown (including the load and parasitic effects). After defining the pulse width modulation in terms of a reverse mode-dependent dwell time, an elementarytime-unit Lyapunov function is used to derive a set of linear matrix inequalities (LMIs) based on global uniformly ultimately boundedness of the switched system. The LMIs are solved in an adaptive fashion using an exploitation-exploration mechanism: exploitation is achieved by solving the LMIs based on the estimated switched model, while exploration is achieved by a persistently exciting input voltage source, which guarantees convergence of the estimated parameters to the true system parameters.

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Section: Switched Dynamics Parametric Uncertainty and Related Workmentioning

confidence: 99%

Section: Switched Dynamics Parametric Uncertainty and Related Workmentioning

confidence: 99%

Adaptive pulse width modulation design for power converters based on affine switched systems

Baldi

Papachristodoulou

Kosmatopoulos

2018

Nonlinear Analysis: Hybrid Systems

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“…Proposition 2 [22,Proposition 3]. The system (7) under the set-valued control law (13)- (16) is KL-stable in Z.…”

Section: Problemmentioning

confidence: 99%

“…n.athanasopoulos@tue.nl, m.lazar@tue.nl controlled (k, λ)-contractiveness [21], [22]. For discretetime homogeneous systems, the sets having these properties are also regions of attraction or regions of stabilizability.…”

Section: Introductionmentioning

confidence: 99%

On controlled-invariance and stabilization of time-delay systems

Αθανασόπουλος

Lazăr

2014

2014 European Control Conference (ECC)

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Abstract-A non-conservative synthesis approach for discrete-time linear time-delay systems is presented, induced by a relaxed notion of invariance, namely, controlled (k, λ)-D-contractiveness. We characterize two particular families of controlled (k, λ)-contractive sets in the augmented state space of the corresponding delay-free system and establish their relationship to controlled (k, λ)-D-contractive sets of the timedelay system. The required computations for both the controller synthesis and controller implementation are carried in the state space of the time-delay system, making the method scalable with respect to the maximum delay.

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“…The equivalence between controlled (k, λ)-contractive proper C-sets and finite-time CLFs is formally stated next. Proposition 4. , Athanasopoulos et al (2013)]. Consider the linear system (3) and a proper C-set S. The following statements are equivalent.…”

Section: Preliminariesmentioning

confidence: 99%

Scalable Stabilization of Large Scale Discrete-time Linear Systems via the 1-norm

Αθανασόπουλος

Lazăr

2013

IFAC Proceedings Volumes

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This article reconsiders the stabilizing controller synthesis problem for discrete-time linear systems with a focus on systems of large scale. In this case, existing solutions are either not scalable, and thus, not tractable, or conservative. This motivates us to exploit finite-time control Lyapunov functions (CLFs), i.e., a relaxation of the standard CLF concept, to obtain a nonconservative and scalable synthesis method. The main idea is to employ Minkowski functions of a particular family of polytopic sets, which includes the hyper-rhombus induced by the 1-norm, as candidate finite-time CLFs. This choice results in explicit periodic vertex-interpolation control laws, which are globally stabilizing. The vertex-control laws can be computed offline using distributed optimization, in a scalable fashion, while the actual control law comes in an explicit, distributed form. Large scale illustrative examples demonstrate the effectiveness of the proposed approach.

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On constrained stabilization of discrete-time linear systems

Cited by 6 publications

References 23 publications

Adaptive pulse width modulation design for power converters based on affine switched systems

Adaptive pulse width modulation design for power converters based on affine switched systems

On controlled-invariance and stabilization of time-delay systems

Scalable Stabilization of Large Scale Discrete-time Linear Systems via the 1-norm

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