## Weekly outline

• ### BE3M35LSY - Linear Systems

The purpose of this course is to introduce mathematical tools for the description, analysis, and partly also synthesis, of dynamical systems. The focus will be on linear time-invariant multi-input multi-output systems and their properties such as stability, controllability, observability and state realization. State feedback, state estimation, and the design of stabilizing controllers will be explained in detail. Partially covered will be also time-varying and nonlinear systems. Some of the tools introduced in this course are readily applicable to engineering problems such as the analysis of controllability and observability in the design of flexible space structures, the design of state feedback in aircraft control, and the estimation of state variables. The main motivation, however, is to pave the way for the advanced courses of the study program. The prerequsites for this course include undergraduate level linear algebra, differential equations, and Laplace and z transforms.

Výsledek studentské ankety předmětu je zde: AE3M35TDS

• ### 1 říjen - 7 říjen

Lecture 1: Systems and signals. Linear and time-invariant systems. Differential and difference systems.

• ### 8 říjen - 14 říjen

Lecture 2: The concept of state, state equations.

• ### 15 říjen - 21 říjen

Lecture 3: Solving the state equations, modes of the system. Equivalence of systems. Continuous-time, discrete-time, and sampled-data systems.

• ### 22 říjen - 28 říjen

Lecture 4: Internal and external stability of systems.

• ### 29 říjen - 4 listopad

Lecture 5: Reachability and controllability of systems.

Lecture 6: Observability and constructibility of systems. Dual systems.

Lecture 7: Standard forms for systems, Kalman’s decomposition.

Lecture 8: Internal and external descriptions of systems, impulse response and transfer function. Poles and zeros of systems.

• ### 26 listopad - 2 prosinec

Lecture 9: State realizations of external descriptions. Minimal realizations, balanced realizations.

• ### 3 prosinec - 9 prosinec

Lecture 10: State feedback, optimal state regulation, pole assignment.

• ### 10 prosinec - 16 prosinec

Lecture 11: Output injection, state estimation.

• ### 17 prosinec - 23 prosinec

Lecture 12: Interconnection of systems, feedback controllers, stabilizing controllers.

• ### 24 prosinec - 30 prosinec

Lecture 13: State representation of stabilizing controllers, separation property of state regulation and estimation.