Differential Algebraic Equations

Resources: Modelling and Simulation Lecture Notes.pdf Ch.2

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Semi-explicit form

$$\begin{array}{rl}\dot{x}& =f(x,z,u)\\ 0& =c(q,z)\end{array}$$

Where

• $z$ are the algebraic states (i.e states that does not make a time differentiated appearance in the set of equations).
• $u$ are a set of inputs.

Idea: In order to evaluate $f(x,z,u)$, we need to know $z$. → The idea is to use $0=c(z,x)$ to solve for $z$ and insert it into $f$

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Terms

Differential Index