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Analysis and Control of Linear Systems via LMIs

This project presents some codes developed during the course on Analysis and Control of Linear Systems via Linear Matrix Inequalities (LMIs) Optimization (2022.1) - Master's Program in Electrical Engineering - Federal University of Ceara.

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💻 Requirements to start this project:

Before starting, make sure you've met the following requirements:

🔍 References

  • Linear Matrix Inequalities in System and Control Theory - Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Venkataramanan Balakrishnan
  • Mixed H2/Hinf control of a two-floors building model using the linear matrix inequality approach - Gustavo Luiz Chagas Manhães de Abreu, Vicente Lopes Jr., Michael J. Brennan
  • Analysis and Control of Linear Systems via Linear Matrix Inequalities (LMIs) Optimization course lecture notes - Prof. Fabrício Gonzalez Nogueira (2022.1) - Master's Program in Electrical Engineering - Federal University of Ceara.
  • https://github.com/iuricode/README-template/blob/main/README-repository/iuricode.md

📝 License

This project is under license. See the LICENSE file for more details.

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Tasks - LMI Final Project 1

  • Task 1: D-Stability with polytopic uncertainties

    • Choosing a linear state space model;
    • Specifying performance requirements for the closed loop system;
    • Defining a D-Stability region for the closed-loop poles;
    • Defining the corresponding LMI problem;
    • Defining parametric polytopic uncertainties;
    • Including state-feedback integral action by finding the augmented space state model;
    • Verifying reference tracking and disturbance rejection for different polytope points.
  • Task 2: Robust control

    • Including the LMI conditions for the mixed H2-Hinf Control

Tasks

The project is still under development and the next updates will focus on the following tasks:

  • Creating a github repository for the project
  • Adapting the structure of this readme to the project needs
  • Adopting git best practices in the repository
  • Adding more references
  • Implementing integral action in the polytopic case (using D-Stability) for reference tracking
  • Implementing the H2/Hinf algorithm for the building vibration control

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