State-space linearization example

1. What is state-space example?
2. How do you Linearize a nonlinear state-space model?

What is state-space example?

Exploring a state space is the process of enumerating possible states in search of a goal state. The state space of Pacman, for example, contains a goal state whenever all food pellets have been eaten, and is explored by moving Pacman around the board.

How do you Linearize a nonlinear state-space model?

Linearization of State-Space Models

˙x=f(x,u)(nonlinear state-space model)x=(x1⋮xn),u=(u1⋮um),f=(f1⋮fn), we can apply Taylor expansion in multivariables. Assume x=0,u=0 is an equilibrium point: f(0,0)=0, i.e., when the system is at rest and no control is applied, the system does not move.