# Introduction to state space models and their use in systems analysis and control

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This chapter gives a summary of key methods and concepts around state space models. The content is primarily a targeted at students doing a single course in state space methods and hence does not dwell on some fine details which would be covered in a 2nd course or in research applications; one such example is non-simple Jordan forms and another is finding approximate state space models by linearisation of 1st principles models. Once the principles are understood clearly, Students are encouraged to use tools like MATLAB for some of the number crunching as manipulation of state space models is not a paper and pen exercise in general.

The focus of these sections is on state space analysis methods. This begins with definitions and origins of state space models alongside a discussion of their equivalences with transfer function models. This is followed by analysis of the associated system behaviours and links to the state space model parameters. The final sections focus on control design and thus concepts such as controllability, observability and control design methods.

- Definitions of state space models.
- Behaviours of state space models.
- Controllability and observability.
- Control design and observer design.
- Optimal control design - IN PROGRESS.
- Use of MATLAB for control

It is implicit in several of these chapters that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace. More information on these can be found in the Mathematics theme of the left hand toolbar.