Linear Systems

By Panos J. Antsaklis, Anthony N. Michel. Scientific Parallel Computing, 2010

766 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/fb38f320a127d31a086ddcd616cd9080e3de0453

Citations in the corpus

Multiplicity-induced-dominancy for delay-differential equations of retarded type (2020, neutral): “Polynomial interpolation problems are known to be useful in the control of dynamical systems, as illustrated in [28, p. 121], where the controllability of a ﬁnite-dimensional dynamical system is characterized in terms of the invertibility of a Vandermonde matrix (see also [24]).”
Using Inertial Sensors for Position and Orientation Estimation (2017, neutral): “The concept of identifiability is closely related to the concept of observability which is concerned with the question of if the time-varying states can be determined from the available data [69].”
Exact controllability of complex networks (2013, neutral): “Thus, it is reasonable to assume random-weight distributions rather denotes the minimum number of drivers calculated from the maximum algebraic multiplicity. q = 1 , 2 , · · · , N and the algebraic multiplicity of eigenvalues is indicated in “()” for star and fully connected networks.”
A Survey of Model Reduction by Balanced Truncation and Some New Results (2004, neutral): “It follows that (see Kailath 1980, Gawronski and Juang 1990) cðtÞ ¼ P ScðtÞPScðtÞT where ScðtÞ :¼ eAt: From the definition of PT in (64), we obtain PT ¼ cðt2Þ cðt1Þ ¼ Scðt1ÞPScðt1ÞT Scðt2ÞPScðt2ÞT ð65Þ ¼ ð1 0 eA eAt1BBTeA Tt1 eAt2BBTeA Tt2…”
Adaptation, Learning, and Optimization over Networks (2014, neutral): “Interested readers may consult the works [132, 133, 149, 150] and the many references therein for additional information.”
Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle (2009, neutral): “By the detectability of (H,A− (ρ/2)I), it is straightforward to show that the pair (H1, A11 − (ρ/2)I) and hence (H1, A11) are observable (see [23, 37]).”
Characterizing the Codimension of Zero Singularities for Time-Delay Systems (2016, neutral): “The explicit development of numeric/symbolic algorithms for LU factorization and inversion of the confluent Vandermonde and Birkhoff matrices [29, 33–35] is still an attracting topic due to their specific structure and their implications in various applications, see for instance [27, 36] and referen”
Designing and Modeling for Power Integrity (2010, neutral): “Once the coefficients {bm} are known, the zeros {q′ m} of the denominator in (23) are computed using standard methods [55], [56], and the process is repeated by”
Spectral equivalence of matrix polynomials and the index sum theorem (2014, neutral): “These play an important role in a number of applications in systems and control theory [12, 24, 50, 51], but they are not preserved in general by linearizations, in contrast to elementary divisors.”
Control and Communication Challenges in Networked Real-Time Systems (2007, neutral): “For a general introduction to control and to linear and nonlinear system theory see [5], [49], [51], [69], [104], and [107].”
A Comparative Study of Passivity Enforcement Schemes for Linear Lumped Macromodels (2008, neutral): “The standard choice is to minimize the global energy (squared -norm) in the model perturbation , which can be expressed as (31) where is the controllability Gramian [13] associated to (1).”
On the generation of large passive macromodels for complex interconnect structures (2006, neutral): “However, an obvious coordinate change [24], [29] can be applied to recover a purely real realization”
Controllability Metrics, Limitations and Algorithms for Complex Networks (2013, neutral): “To formalize this discussion, deﬁne the T -steps controllability Gramian by It can be veriﬁed that the controllability Gramian W K ,T is positive deﬁnite if and only if the network is controllable in T steps by the nodes K [1].”
On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times (2009, neutral): “…with components With this definition the demand model can directly be transformed into an observable canonical state space form where D is a (2×2) left companion matrix (see for instance Kailath, 1980) with and E is a two dimensional vector with Here ( ) T  is the transpose of a vector or matrix.”
On Submodularity and Controllability in Complex Dynamical Networks (2014, neutral): “The material in this section is mostly standard and can be found in many texts on linear system theory, e.g. [17], [3]; we discuss the material mostly to set our notation.”
Control Principles of Complex Networks (2015, neutral): “Hence, the number of control inputs must be greater than or equal to the largest geometric multiplicity of the eigenvalues of A (Antsaklis and Michel, 1997; Sontag, 1998; Yuan et al., 2013).”