Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions.
MAT Functional Analysis
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Solution Manual for Linear Systems Theory – João Hespanha
Description: Linear spaces and operators, mathematical descriptions of linear systems, controllability and observability, irreducible realization of rational transfer-function matrices, canonical forms, state feedback and state estimators, and stability. Prerequisite: Knowledge of linear algebra, differential equations, and feedback control systems e. ECE Instructor: Dr. Zhi-Hong Mao, office Benedum Hall, phone , email maozh engr.
This course provides an introduction to the modern state space theory of linear systems for students of circuits, communications, controls, and signal processing. In some sense it is a second course in linear systems, since it builds on an understanding that students have seen linear systems in use in at least some context before. The course is on the one hand quite classical and develops some rather well developed material, but on the other hand is quite modern and topical in that it provides a sense of the new vistas in embedded systems, computer vision, hybrid systems, distributed control, game theory and other current areas of strong research activity. Topics include: A review of linear algebra and matrix theory.