## CME 263: Introduction to Linear Dynamical Systems (EE 263)

Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in
EE 103 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.

Terms: Aut, Sum
| Units: 3

Instructors:
Aggarwal, G. (PI)
;
Lall, S. (PI)
;
Kim, J. (TA)
;
Luxenberg, E. (TA)
;
Tuck, J. (TA)
;
Zhang, J. (TA)

## CME 345: Model Reduction

Model reduction is an indispensable tool for computational-based design and optimization, statistical analysis, embedded computing, and real-time optimal control. This course presents the basic mathematical theory for projection-based model reduction. Topics include: notions of linear dynamical systems and projection; projection-based model reduction; error analysis; proper orthogonal decomposition; Hankel operator and balancing of a linear dynamical system; balanced truncation method: modal truncation and other reduction methods for linear oscillators; model reduction via moment matching methods based on Krylov subspaces; introduction to model reduction of parametric systems and notions of nonlinear model reduction. Course material is complemented by a balanced set of theoretical, algorithmic and Matlab computer programming assignments. Prerequisites:
CME 200 or equivalent,
CME 263 or equivalent and basic numerical methods for ODEs.

Last offered: Spring 2017

## EE 263: Introduction to Linear Dynamical Systems (CME 263)

Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in
EE 103 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.

Terms: Aut, Sum
| Units: 3

Instructors:
Aggarwal, G. (PI)
;
Lall, S. (PI)
;
Kim, J. (TA)
;
Luxenberg, E. (TA)
;
Tuck, J. (TA)
;
Zhang, J. (TA)

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