State-Space Models

Lecture slides: state-space-models.pdf Download state-space-models.pdf

Reading suggestion: KJA_pp139_150.pdf Download KJA_pp139_150.pdf

We first introduce the state-space models, and confirm that transfer function models and state-space models are really describing the same thing. State-space models just offer a different perspective, and unlock a range of powerful tools from linear algebra that we can now use for system analysis.

Next we translate a few concepts from transfer functions into the state-space world by showing that poles and zeros can be determined from a state-space model by solving eigenvalue problems.

A curious point here is that this shows something deeper than the observation that transfer functions and state-space give useful perspectives on the same object. It is really saying that linear algebra and complex-analysis give different viewpoints on the same mathematics. We will another example of this when we study coordinate changes.

An important tool in the analysis of state-space models are coordinate changes. These can be used to change the coordinates of the state variable in a way that reveals more structural features about the A, B, C and D matrices. We've already seen one example of this - the controllable canonical form. We review another which can be used to perform partial fraction expansion with eigenvalue analysis.