DAEs in Circuit Modelling: A Survey

Riaza, Ricardo

doi:10.1007/978-3-642-34928-7_3

Cited by 10 publications

(13 citation statements)

References 151 publications

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“…It is worth to observe that, once the memristor parameters a and b are fixed, the equilibrium points (58)-(60) can move along the ϕ M axis if and only if Q 0 varies. It follows that no bifurcations due to the initial conditions 15…”

Section: Remarkmentioning

confidence: 95%

“…Circuit analysis methods based on DAEs are fundamental in numerical simulation (using, e.g., PSpice software) of linear and nonlinear circuits [15]. On the other hand, qualitative nonlinear aspects (e.g., the existence of no-finite-forward-escapetime solutions, eventual uniform-boundedness of solutions, local and global asymptotic stability properties, bifurcation phenomena, etc.)…”

Section: B State Equations In the (ϕ Q)-domainmentioning

confidence: 99%

“…Stability properties of attractors, local and global bifurcations, and the role of the initial conditions have been extensively investigated as well [14]. A systematic description (mainly based on the network theory technique referred to as the tableau method) is proposed in [15], but this leads to large systems of nonlinear Differential Algebraic Equations (DAEs), whose solution requires efficient numerical simulation tools.…”

Section: Introductionmentioning

confidence: 99%

“…Given a circuit in the class LM, with fixed topology for t ≥ t 0 , our goal is to develop a method to analyze its dynamics for t ≥ t 0 . An illustrative example allows us to highlight the key issues addressed by the proposed methodology and its advantages over current approaches (see in particular [8], [9], [15]).…”

Section: Introductionmentioning

confidence: 99%

“…for any t ≥ t 0 , where v k (t) is the voltage across and i k (t) is current through any two-terminal element in LM, respectively; • the use of Constitutive Relations (CRs) expressed according to the same electrical variables, that is, CRs of resistors, capacitors, inductors, and memristors specified in terms of incremental charges and fluxes. The main advantage of the proposed method is that it enables to describe memristor-based circuits in the class LM by means of IVPs for a reduced number of ODEs compared to current approaches available in literature (e.g., [8] and [15]). This permits to simplify the investigation of nonlinear dynamic behavior and bifurcation phenomena in memristor circuits and to make clear the influence of initial conditions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Memristor Circuits: Flux—Charge Analysis Method

Corinto

Forti

2016

IEEE Trans. Circuits Syst. I

123

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Section: Remarkmentioning

confidence: 95%

Section: B State Equations In the (ϕ Q)-domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Memristor Circuits: Flux—Charge Analysis Method

Corinto

Forti

2016

IEEE Trans. Circuits Syst. I

123

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Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs—Application to secure communications

Moysis

Gupta

Mishra

et al. 2020

Intl J Robust & Nonlinear

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This work considers the problem of observer design for rectangular descriptor systems with nonlinearities satisfying incremental quadratic constraints. The observer design is feasible under the satisfaction of a linear matrix inequality and some algebraic relations in the system matrices. The special case of nonlinearities in the output is also considered. Finally, the developed approach is applied to the problem of secure communications and illustrated through numerical examples.

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Normal forms and internal regularization of nonlinear differential‐algebraic control systems

Chen

Trenn

Respondek

2021

Intl J Robust & Nonlinear

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In this article, we propose two normal forms for nonlinear differential‐algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, that is, when there exists a state feedback transforming the DACS into a differential‐algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs.

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DAEs in Circuit Modelling: A Survey

Cited by 10 publications

References 151 publications

Memristor Circuits: Flux—Charge Analysis Method

Memristor Circuits: Flux—Charge Analysis Method

Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs—Application to secure communications

Normal forms and internal regularization of nonlinear differential‐algebraic control systems

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