Geometric Analysis of Differential-Algebraic Equations via Linear Control Theory

DOI10.1137/20M1329330zbMath1472.34018arXiv2002.00689WikidataQ115246901 ScholiaQ115246901MaRDI QIDQ5855526

Witold Respondek, Yahao Chen

Publication date: 18 March 2021

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00689

zbMATH Keywords

differential-algebraic equationsinvariant subspacescontrol systemssingular systemsKronecker canonical formimplicit systemsMorse canonical form

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Linear systems in control theory (93C05) Implicit ordinary differential equations, differential-algebraic equations (34A09) Control problems involving ordinary differential equations (34H05) Linear ordinary differential equations and systems (34A30) Control/observation systems governed by ordinary differential equations (93C15)

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On Characteristic Invariants of Matrix Pencils and Linear Relations, Normal forms and internal regularization of nonlinear differential‐algebraic control systems, Feedback linearization of nonlinear differential‐algebraic control systems, On impulse-free solutions and stability of switched nonlinear differential-algebraic equations, From Morse triangular form of ODE control systems to feedback canonical form of DAE control systems, Geometric analysis of nonlinear differential-algebraic equations via nonlinear control theory, Impulse-free jump solutions of nonlinear differential-algebraic equations

Cites Work

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• The quasi-Weierstrass form for regular matrix pencils
• Controlled invariance for nonlinear differential-algebraic systems
• A tutorial on the geometric analysis of linear time-invariant implicit systems
• Linear multivariable control. A geometric approach
• The eigenvalue problem \(\lambda Tx+Sx\)
• On an existence and uniqueness theory for nonlinear differential- algebraic equations
• A geometric treatment of implicit differential-algebraic equations
• Proportional and proportional-derivative canonical forms for descriptor systems with outputs
• A survey of linear singular systems
• Generalized linear systems: Geometric and structural approaches
• Regularization of linear time-invariant differential-algebraic systems
• On a geometrical interpretation of differential-algebraic equations
• The Quasi-Kronecker Form For Matrix Pencils
• Matrix pencil characterization of almost ( A, Z) -invariant subspaces : A classification of geometric concepts
• Some geometric considerations about the Kronecker normal form
• A strong controllability and observability in linear multivariable control
• Structural invariants of linear multivariable systems
• Solution Concepts for Linear DAEs: A Survey
• Addition to “The Quasi-Kronecker Form for Matrix Pencils
• Decoupling and Pole Assignment in Linear Multivariable Systems: A Geometric Approach
• Structural Invariants of Linear Multivariable Systems