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Journal Article•DOI An optimal control approach to robust control design Feng Lin 01 Jan 2000-International Journal of Control 91 Citations	Our approach can deal with both linear and non-linear systems.
Journal Article•DOI On the Universality of Axon P Systems Xingyi Zhang, Linqiang Pan, Andrei Păun - Show less +2 more 10 Feb 2015-IEEE Transactions on Neural Networks 136 Citations	These results illustrate that the simple linear structure is enough for axon P systems to achieve a desired computational power.
Proceedings Article•DOI Additive Decomposition and its applications to internal-model-based tracking Quan Quan, Kai-Yuan Cai - Show less +1 more 01 Dec 2009 26 Citations	Therefore, various special tools for analyzing linear systems can be applied to the first subproblem which is helpful to the designers.
Journal Article•DOI Two for Review: Linear Systems & Automatic Generation (review of "Linear Systems" ; Bourles, H.; 2010) [Book Reviews] Luis Rouco 01 Nov 2011-IEEE Power & Energy Magazine 1 Citations	This book can be very useful to build two graduate course on linear systems.
Open access•Journal Article•DOI Stationary and Ergodic Properties of Stochastic NonLinear Systems Controlled over Communication Channels Serdar Yüksel 19 Oct 2016-Siam Journal on Control and Optimization 15 Citations	The findings generalize existing results for linear systems.
Journal Article•DOI Harnessing piecewise-linear systems to construct dynamic logic architecture. Haipeng Peng, Yixian Yang, Lixiang Li, Hong Luo - Show less +3 more 11 Jul 2008-Chaos 18 Citations	It is convenient for us to study and analyze them with the theory of linear systems.
Open access•Journal Article•DOI Finite Dimensional State Representation of Linear and Nonlinear Delay Systems Odo Diekmann, Mats Gyllenberg, Johan A. J. Metz, Johan A. J. Metz, Johan A. J. Metz - Show less +4 more 01 Dec 2018-Journal of Dynamics and Differential Equations 28 Citations	Our results on linear systems with input and nonlinear systems are new.
Proceedings Article•DOI Computing reachable sets of linear vector fields revisited Ting Gan, Mingshuai Chen, Yangjia Li, Bican Xia, Naijun Zhan - Show less +4 more 01 Jun 2016 10 Citations	Comparing with existing abstractions for linear dynamical systems, experimental results indicate that our abstraction is more precise.
Journal Article•DOI Fast recursive algorithms for a class of linear equations George Carayannis, Nicholas Kalouptsidis, Dimitris G. Manolakis - Show less +2 more 01 Apr 1982-IEEE Transactions on Acoustics, Speech, and Signal Processing 90 Citations	These techniques have common characteristics so that they may be generalized to cover a wider class of linear systems.

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Is math difficult?5 answersMath difficulties are prevalent and multifaceted, encompassing various cognitive weaknesses in mathematical domains. Research highlights that math learning difficulty (MLD) is a distinct learning disorder characterized by impairments in number understanding and application, independent of intelligence or schooling. These difficulties manifest in computation, number sense, and visual-spatial short-term storage, with no particular strengths identified. Factors contributing to math learning difficulties include innate cognitive abilities, problem-solving processes, external factors like fear and anxiety, weak foundations, and instructional quality. Additionally, dyscalculia, a form of mathematical difficulty, is akin to dyslexia and can be identified through EEG signal analysis, particularly focusing on theta and alpha band amplitudes. Overall, the challenges in learning mathematics encompass conceptual understanding, application of principles, problem-solving, and algorithm mastery.

What are the main challenges in linear algebra?5 answersThe main challenges in linear algebra include the need for more practical and computable approaches to teaching the subject. There is a call for a switch from abstract algebraic taught classes to a concrete matrix-based first course. Additionally, the overemphasis on determinants, characteristic polynomials, and polynomial root finding methods in textbooks is seen as useless and unnecessary. The teaching of linear algebra should focus on problem-solving strategies such as looking for invariants, checking parity, and defining energy functions. Another challenge is the need for clear definitions and explanations of key theorems and concepts in linear algebra, as well as providing diverse and challenging example problems for students.

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Why we need exact linearization of Nonlinear Systems?4 answersExact linearization of nonlinear systems is necessary for several reasons. Firstly, it allows for the application of elegant solution methods in the Laplace- and z-domain, which are only applicable to linear systems. Secondly, exact linearization enables the use of linear controllers to achieve control objectives, eliminating the need for complex nonlinear controllers. Additionally, linearization is useful when system components do not exhibit linear behavior, as it allows for the derivation of linear approximations for these components. This is particularly important in feedback control systems, where linear approximations can be used to keep the system near a defined operating point. Overall, exact linearization of nonlinear systems provides a valuable tool for design engineers to simplify control and analysis tasks.

What are Linear A and B systems?5 answersLinear A and B systems are different types of systems that are studied in various fields. Linear A is a system of writing that has not been deciphered yet, but it is believed to have both administrative and votive texts. On the other hand, Linear B is a system of writing that has been partially deciphered and mainly consists of administrative texts. The study of Linear A has been aided by comparing it to the known texts in Linear B, but caution must be exercised as there are significant differences between the two systems in terms of document types and epigraphy. In a different context, Linear systems are also studied in the field of algebra, where B-systems are algebras that are constructively equivalent to contextual categories and are closer to the structures modeled by type theories. Additionally, linear systems are also studied in the field of control theory, where the problem of confining the trajectory of a linear discrete-time system in a given polyhedral domain is addressed through the concept of (A, B)-invariance.

Is math hard?5 answersMathematics is often perceived as difficult by many students. This perception is not surprising, as some children experience learning difficulties and disabilities in math. However, it is important to consider other factors that contribute to the perception of math being hard. One study found that students in a Caribbean setting attributed their dislike of math to the belief that their teachers were "making mathematics hard". Additionally, research suggests that the way math is taught in elementary education may contribute to its perceived difficulty. Conventional wisdom suggests that math is inherently difficult, but experts argue that the educational system may actually hinder skill development in math. Therefore, while math can be challenging for some individuals, it is important to consider various factors that influence this perception.

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