# A brief and practical introduction to H-infinity Control

It is a practical introduction to H-infinity control for people who already know classical control (transfer functions, Bode plots, loop shaping).
The emphasis is on *how* to use H-infinity synthesis to design controllers, rather than on the underlying theory.

- Lecture notes (PDF): [index.pdf](index.pdf)
- Video recording: [YouTube](https://www.youtube.com/watch?v=KdJsm_X8uks)

## Content

1. **Introduction to Model Based Control**: methodology, from classical to robust control, and the example system (a mass-spring-damper with an actuator) used throughout the lecture.
2. **Classical Open Loop Shaping**: manual loop shaping and H-infinity loop shaping synthesis.
3. **A first step into the H-infinity world**: the H-infinity norm, H-infinity synthesis, and the generalized plant.
4. **Modern interpretation of control specifications**: closed-loop transfer functions (gang of four), the sensitivity function, and the module margin.
5. **H-infinity shaping of closed-loop transfer functions**: design of weighting functions and their limitations.
6. **Mixed-sensitivity H-infinity control**: a complete step-by-step design example (shaping of S, then GS, then T).

Each chapter contains exercises, with hints and solutions.

## Running the Matlab scripts

### Requirements

- Matlab R2019b or newer
- Control System Toolbox
- Robust Control Toolbox

### Scripts

There is one script per chapter, plus a helper function:

| Script                                     | Chapter                                         |
|--------------------------------------------|-------------------------------------------------|
| `h_infinity_1_open_loop_shaping.m`         | Classical Open Loop Shaping                     |
| `h_infinity_2_control_specifications.m`    | Modern Interpretation of Control Specifications |
| `h_infinity_3_shaping_cl_tf.m`             | H-infinity Shaping of closed-loop transfer functions |
| `h_infinity_4_mixed_sensitivity_example.m` | Mixed-Sensitivity H-infinity Control - Example  |