Guide Differential-algebraic systems: Analytical aspects and circuit applications

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Zero dynamics and funnel control of linear differential-algebraic systems. Original Article First Online: 10 April This is a preview of subscription content, log in to check access. Berger T, Ilchmann A, Reis T Normal forms, high-gain and funnel control for linear differential-algebraic systems. Bernstein DS Matrix mathematics: theory, facts, and formulas, 2nd edn.

North-Holland, Amsterdam Google Scholar. Campbell SL Singular systems of differential equations I.

Chapter 3. Differential-Algebraic-Equation-Systems and Multiport Method

Pitman, New York Google Scholar. Cobb DJ Controllability, observability and duality in singular systems.

Dai L Singular control systems. Lecture notes in control and information sciences, vol Springer, Berlin Google Scholar. Teubner, Stuttgart Google Scholar.

Applications to Systems of Differential Equations

Modelling, state space analysis, stability and robustness, vol Texts in applied mathematics. Isidori A Nonlinear control systems, communications and control engineering series, 3rd edn. Kunkel P, Mehrmann V Differential-algebraic equations. Analysis and numerical solution. Due to the strong relation to ordinary differential equations, the literature for DAEs mainly started out from introductory textbooks. As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in.

Table of Contents

The results in the individual chapters are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students with a good knowledge of the basic principles of DAEs for self-study. Springer Professional. Back to the search result list. As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in - Controllability for linear DAEs - Port-Hamiltonian differential-algebraic systems - Robustness of DAEs - Solution concepts for DAEs - DAEs in circuit modeling.

Different concepts related to controllability of differential-algebraic equations are described. The class of systems considered consists of linear differential-algebraic equations with constant coefficients.


  1. Mathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory L. D Faddeev B0000EG1RR.
  2. AMS :: Mathematics of Computation!
  3. Zero dynamics and funnel control of linear differential-algebraic systems;

The concepts of impulse controllability, controllability at infinity, behavioral controllability, and strong and complete controllability are described and defined in the time domain. Equivalent criteria that generalize the Hautus test are presented and proved.

Melnikov theory for weakly coupled nonlinear RLC circuits

Special emphasis is placed on normal forms under state space transformation and, further, under state space, input and feedback transformations. Consequences for state feedback design and geometric interpretation of the space of reachable states in terms of invariant subspaces are proved. This paper presents a survey of recent results on the robust stability analysis and the distance to instability for linear time-invariant and time-varying differential-algebraic equations DAEs.

Different stability concepts such as exponential and asymptotic stability are studied and their robustness is analyzed under general as well as restricted sets of real or complex perturbations. Formulas for the distances are presented whenever these are available and the continuity of the distances in terms of the data is discussed.

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