Stability analysis in continuous and discrete time

Besseling, N.C.

doi:10.3990/1.9789036533072

Cited by 9 publications

(3 citation statements)

References 25 publications

(36 reference statements)

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“…In this transformation, the stable (unstable) eigenvalues of A e , which lie on the left (right) half plane, are mapped onto the interior (exterior) of the unit circle. In addition to this transformation from continuous to discrete infinite dimensional system representation, the Cayley transformation maps the unbounded operators A e and B e into their bounded, infinite dimensional counterparts Φ and Γ, respectively [29].…”

Section: Model Predictive Controlmentioning

confidence: 99%

Model predictive control of the cardiac amplitude of alternans PDE

Yapari

Dubljević

2014

2014 American Control Conference

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Sudden cardiac death resulting from ventricular arrhythmia is one of the leading causes of mortality in the United States. The beat-to-beat oscillations in the action potential duration (APD) of paced cardiac cells, defined as cardiac alternans, has been identified as a potential precursor to ventricular arrhythmia. Therefore, the annihilation of these alternans is a promising antiarrhythmic strategy. In this work, the small amplitude of alternans partial differential equation (PDE) for a one dimensional cable of cardiac cells is stabilized through model predictive control (MPC). In our proposed control strategy, both boundary and spatially distributed actuators are utilized in suppressing the alternans along the cable. The loworder MPC formulation is developed for the finite-dimensional, discrete state space representation of the PDE. Furthermore, input and state constraints are addressed explicitly in the MPC formulation. The input constraints may arise due to actuator limitations, while state constraints are naturally present in cardiac systems. By satisfying these constraints, we can ensure that the controller action will not induce conduction block in the cardiac cells. Simulation results are presented to demonstrate the successful annihilation of alternans using the proposed control algorithm.

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Section: Model Predictive Controlmentioning

confidence: 99%

Model predictive control of the cardiac amplitude of alternans PDE

Yapari

Dubljević

2014

2014 American Control Conference

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“…From [27,28], it was shown that a stable continuous operator generates a stable discrete operator, thus, if (A + BK) is stable, then the discrete operatorĀ d = −I + 2δ (δI − A − BK) −1 is stable as well. Finally, if the control law proposed in Equation (53) with K d shown in Equation (54), is used, then the closed-loop discrete operator is equivalent to the operator shown above and the discrete closed-loop system is stable as well (i.e.,…”

Section: Discrete System Stabilizationmentioning

confidence: 99%

Discrete Output Regulator Design for the Linearized Saint–Venant–Exner Model

Cassol

Dubljević

2020

Processes

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This manuscript addresses the regulator design in the discrete-time setting for the unstable linearized Saint–Venant–Exner model, which describes the dynamics of a sediment-filled water canal. The proposed regulator ensures the closed-loop stability and proper tracking of polynomial and periodic reference signals using output feedback in a sample-data setting. To design this regulator, the system discrete representation is achieved by the application of the structure-preserving Cayley-Tustin time discretization and the direct relation with the regulator in the continuous-time setting is shown. The regulator design in the continuous-time setting is developed using the backstepping methodology ensuring the closed-loop stability and the observer design, while the Sylvester equations are solved to achieve proper tracking. Finally, the numerical simulation results are presented to show the performance of the regulator.

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“…Nice identities between the powers of the cogenerator and integral expressions which involve generalized Laguerre polynomials appear in [17, Theorem 1], [6,Lemma 4.4] and [5,Lemma 6.7].…”

Section: -Semigroups and Resolvent Operators Given By Laguerre Expans...mentioning

confidence: 99%

$C_0$-semigroups and resolvent operators approximated by Laguerre expansions

Abadías¹,

Miana²

2013

Preprint

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In this paper we introduce Laguerre expansions to approximate vector-valued functions expanding on the well-known scalar theorem. We apply this result to approximate C0semigroups and resolvent operators in abstract Banach spaces. We study certain Laguerre functions, its Laplace transforms and the convergence of Laguerre series in Lebesgue spaces. The concluding section of this paper is devote to consider some examples of C0-semigroups: shift, convolution and holomorphic semigroups where some of these results are improved.

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Stability analysis in continuous and discrete time

Cited by 9 publications

References 25 publications

Model predictive control of the cardiac amplitude of alternans PDE

Model predictive control of the cardiac amplitude of alternans PDE

Discrete Output Regulator Design for the Linearized Saint–Venant–Exner Model

$C_0$-semigroups and resolvent operators approximated by Laguerre expansions

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