**(ME EN 5210/6210 & CH EN 5203/6203)**

In State-Space Control Systems, we will learn how to analyze and design systems expressed as coupled linear first-order differential equations. As an alternative to Classical Control Systems (ME EN 5200/6200), which makes use of the Laplace transform to analyze and design single-input/single-output systems, state-space methods enable us to analyze and design multi-input/multi-output systems in time domain. We will consider both continuous-time and discrete-time equations. Control systems are used to regulate the temperature in a room, to command a robot arm along a desired trajectory, to autopilot an airplane, and to ensure that manufacturing processes stay within specifications. A course in control systems provides a student with a common language with which to qualitatively and quantitatively discuss system performance and specifications. In addition, state-space methods are used to analyze a variety of systems that, at first, seem quite distinct from engineering systems, including economic and social models.

This is not a course about forming state-space models, but rather, analyzing and controlling systems that are already described in state-space form. Other courses exist, at the undergraduate and graduate level, that focus on the topic of forming state-space models for physical systems.

This course is offered every Spring semester.

A course syllabus from the Spring 2016 offering can be found here, which provides the structure of the course and the topics that are covered.

**1. Introduction to Linear Systems**

**2. Modeling Systems in State-Space Form**

**3. Transfer Functions**

**4. Introduction to Discrete Systems**

**5. Fundamentals of Linear Algebra**

**6. Linear Algebraic Equations**

**7. Eigenvectors and Eigenvalues**

**8. Similarity Transformations**

**9. Jordan Form**

**10. Functions of a Square Matrix**

**11. Solutions of Continuous State-Space Equations**

**12. Solutions of Discrete State-Space Equations**

**13. Solutions of Sampled-Data State-Space Equations**

**14. State-Space Realizations of Transfer Functions**

**15. Continuous-Time Bounded-Input Bounded-Output Stability**

**16. Discrete-Time Bounded-Input Bounded-Output Stability**

**17. Continuous-Time Internal Stability**

**18. Discrete-Time Internal Stability**

**19. Controllability in Continuous Time**

**20. Observability in Continuous Time**

**21. Canonical Decomposition of Controllability and Observability**

**22. Controllability and Observability in the Jordan Form**

**23. Controllability of Sampled-data Systems**

**24. State Feedback**

**25. Stabilization**

**26. Tracking**

**27. Robust Tracking with Disturbance Rejection**

**28. State Observers**

**29. Feedback from Estimated States**

**30. Feedback from Estimated States: MIMO Case**

**31. LQR Method**

**32. Kalman Filter (Continuous Time)**

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Page last modified on March 17, 2020, at 12:34 PM