Howtosignalprocessing
- How do you Linearize a nonlinear state-space model?
- Can state-space model nonlinear systems?
- What is the equation for linearization?
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.
Can state-space model nonlinear systems?
The nature of state-space models make them very desirable for analyzing or de- signing a system [18]. First, state-space models can very easily and naturally handle nonlinearity in the model.
What is the equation for linearization?
The Linearization of a function f(x,y) at (a,b) is L(x,y) = f(a,b)+(x−a)fx(a,b)+(y−b)fy(a,b). This is very similar to the familiar formula L(x)=f(a)+f′(a)(x−a) functions of one variable, only with an extra term for the second variable.
