Differential-algebraic systems are generically controllable and stabilizable
نویسندگان
چکیده
Abstract We investigate genericity of various controllability and stabilizability concepts linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations these (see the survey article by Berger Reis (in: Ilchmann A, T (eds) Surveys in equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1 )), we use tools from geometry to characterize terms matrix formats.
منابع مشابه
Differential Algebraic Systems Anew
Linear di erential algebraic equations with properly stated leading term are considered via a decoupling into their essential parts. It is shown why for so-called numerically well formulated equations the decoupling and discretizations commute in some sense. In general one cannot expect this commutativity so that additional diÆculties like strong stepsize restrictions may arise. Moreover, abstr...
متن کاملGenerically Multiple Transitive Algebraic Group Actions
With every nontrivial connected algebraic group G we associate a positive integer gtd(G) called the generic transitivity degree of G and equal to the maximal n such that there is a nontrivial action of G on an irreducible algebraic variety X for which the diagonal action of G on Xn admits an open orbit. We show that gtd(G) 6 2 (respectively, gtd(G) = 1) for all solvable (respectively, nilpotent...
متن کاملSolving Constrained Differential ‐ Algebraic Systems
Trademark Information Visual Numerics, IMSL and PV-WAVE are registered trademarks. JMSL TS-WAVE, and JWAVE are trademarks of Visual Numerics, Inc., in the U.S. and other countries. All other product and company names are trademarks or registered trademarks of their respective owners. The information contained in this document is subject to change without notice. Visual Numerics, Inc. makes no w...
متن کاملAlgebraic Differential Equations and Rational Control Systems
SYSTEMS Yuan Wang Mathematics Department, Florida Atlantic University, Boca Raton, Fl 33431 (407)367-3317, E-mail: y [email protected] Eduardo D. Sontag Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 (908)932-3072, E-mail: [email protected] ABSTRACT An equivalence is shown between realizability of input/output operators by rational control systems and high orde...
متن کاملThomas Decomposition of Algebraic and Differential Systems
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Control, Signals, and Systems
سال: 2021
ISSN: ['0932-4194', '1435-568X']
DOI: https://doi.org/10.1007/s00498-021-00287-x