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Linear systems. --- Amplifiers. --- Electrical engineering.

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"We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigenvalues and admits no non-trivial invariant measure, but is densely distributionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form "diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift" is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties"--

Hilbert space. --- Linear systems. --- Hilbert, Espaces de --- Systèmes linéaires

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Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

Matrices. --- Engineering mathematics. --- Mathematical optimization. --- Linear systems. --- Numerical analysis. --- Dynamics.

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This book covers some selected problems of the descriptor integer and fractional order positive continuous-time and discrete-time systems. The book consists of 3 chapters, 4 appendices and the list of references. Chapter 1 is devoted to descriptor integer order continuous-time and discrete-time linear systems. In Chapter 2, descriptor fractional order continuous-time and discrete-time linear systems are considered. Chapter 3 is devoted to the stability of descriptor continuous-time and discrete-time systems of integer and fractional orders. In Appendix A, extensions of the Cayley-Hamilton theorem for descriptor linear systems are given. Some methods for computation of the Drazin inverse are presented in Appendix B. In Appendix C, some basic definitions and theorems on Laplace transforms and Z-transforms are given. Some properties of the nilpotent matrices are given in Appendix D.

Discrete-time systems. --- Linear time invariant systems. --- Systems, Linear time invariant --- Discrete-time systems --- Linear systems --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems

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Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation. This book develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters.

Adaptive control systems --- Time delay systems --- Linear control systems --- Linear time invariant systems --- Differential equations, Linear. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Linear differential equations --- Linear systems --- Systems, Linear time invariant --- Discrete-time systems --- Automatic control --- Time delay control --- Time delay control systems --- Time delay controllers --- Time-delayed systems --- Feedback control systems --- Process control --- Self-adaptive control systems --- Artificial intelligence --- Self-organizing systems --- Mathematical models. --- Mathematics --- 3D printing. --- Multi-input systems. --- ODE delay notation. --- adaptive control of uncertain systems. --- aerospace engineering. --- backstepping transformation. --- biomedical engineering. --- chemical engineers. --- civil engineering. --- combustion systems. --- computer engineers. --- control designs. --- control synthesis techniques. --- control theorists. --- delay-related challenges. --- delayed telecommunication systems. --- delays in traffic flow dynamics. --- distinct discrete input delays. --- distributed input delays. --- electrical engineers. --- feedback of linear systems. --- finite-dimensional systems. --- global stability of nonlinear infinite-dimensional systems. --- mechanical engineers, aerospace engineers. --- multivariable multidelay systems. --- neuromuscular electrical stimulation. --- nonlinear infinite-dimensional stability study. --- process dynamic researchers. --- robotic manipulators. --- structural engineering. --- supply chains. --- time-delay systems. --- uncertainty combinations. --- unmanned aerial vehicles. --- unmeasured states.