## Weekly outline

• ### BE3M35LSY, AE3M35TDS - Linear Systems, Theory of Dynamical 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 October - 7 October

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

• ### 8 October - 14 October

Lecture 2: The concept of state, state equations.

• ### 15 October - 21 October

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

• ### 22 October - 28 October

Lecture 4: Internal and external stability of systems.

• ### 29 October - 4 November

Lecture 5: Reachability and controllability of systems.

• ### 5 November - 11 November

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

• ### 12 November - 18 November

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

• ### 19 November - 25 November

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

• ### 26 November - 2 December

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

• ### 3 December - 9 December

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

• ### 10 December - 16 December

Lecture 11: Output injection, state estimation.

• ### 17 December - 23 December

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

• ### 24 December - 30 December

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