# How to solve a non-linear system, where state variables are related by H.Ord.Dif.Eqn?

1. Dec 21, 2011

### pairofstrings

1. The problem statement, all variables and given/known data
In control engineering, I want to have a mathematical model of a physical system as a set of input, output and state variables related by higher order differential equations.

2. Relevant concepts
As we all know that, in control engineering, we can solve linear-system using transfer functions. The transfer function is the linear mapping of the Laplace transform of the input, X(s), to the output Y(s). And we use state space models for Multiple input Multiple output systems and/or for non-linear systems. Right?

Y(s) = H(s) X(s)

3. The attempt at a solution

I am able to solve non-linear system using state space representation where mathematical model of a physical system is a set of input, output and state variables are related by first-order differential equations.

But, my question is, how do I solve non-linear system using state space representation where physical system is a set of input, output and state variables are related by higher order differential equations.

Which concepts in mathematics should I refer?

I hope my question is clear. Thanks for the help.

Last edited: Dec 21, 2011
2. Dec 23, 2011

### CEL

Re: How to solve a non-linear system, where state variables are related by H.Ord.Dif.

An nth order differential equation can allways be represented as a set of n first order differential equations.