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# Systems Analysis and Synthesis

## AAE56400

3

### Learning Objective:

To provide the student with basic concepts and techniques used in the modelling, analysis and control design of dynamical systems. Develop state space and transfer function models of physical systems. Analyze systems for stability, controllability, observability and performance. Design feedback controllers for stability, performance and disturbance rejection. Obtain proficiency in related numerical techniques and software.

### Description:

State space methods for modelling, analysis and design of continuous- and discrete-time dynamical systems. Linearization. Stability, controllability, observability, stabilizability, detectability. Pole assignment and state estimation. Lyapunov analysis. Linear quadratic optimal controllers . Use of Matlab/Simulink.

### Topics Covered:

State space modelling of physical systems; Linearization; Transfer functions and their state space realizations; Behavior of linear systems: modes, state transition matrices; Stability; Lyapunov techniques for stability analysis; Controllability and observability; State feedback controllers and stabilizability; Observers and detectability; Output feedback controllers; Disturbance rejection and output tracking; Linear quadratic optimal controllers; Application to aerospace/mechanical systems

### Prerequisites:

Knowledge of linear algebra and differential equations to the level acquired in an undergraduate engineering or science program.

### Applied / Theory:

10 / 90

https://mycourses.purdue.edu

### Web Content:

Syllabus, grades, lecture notes, homework assignments and solutions.

### Homework:

Approximately 1 homework set per week.

None.

### Exams:

1 Midterm and 1 Final Exam

### Textbooks:

No Materials Required.

### Computer Requirements:

ProEd Minimum Computer Requirements, and Matlab/Simulink. Students can access for free via Purdue's Software Remote - https://goremote.ics.purdue.edu.