# NonlinearStateSpaceModel

NonlinearStateSpaceModel[{f,g},x,u]

represents the model , .

gives a state-space representation corresponding to the systems model sys.

NonlinearStateSpaceModel[eqns,{{x1,x10},},{{u1,u10},},{g1,},t]

gives the state-space model of the differential equations eqns with dependent variables xi, input variables ui, operating vaues xi0 and ui0, outputs gi, and independent variable t.

# Details and Options • NonlinearStateSpaceModel is a general representation state-space model.
• NonlinearStateSpaceModel[{f},x,u] assumes .
• NonlinearStateSpaceModel[{f,g},x,u,y,t] explicitly specifies the output variables y and independent variable t.
• NonlinearStateSpaceModel allows for operating values for the states x and inputs u.
• NonlinearStateSpaceModel[,{{x1,x10},},{{u1,u10},},] is used to indicate the operating values for the system.
• In the following systems can be converted:
•  AffineStateSpaceModel exact conversion StateSpaceModel exact conversion TransferFunctionModel exact conversion
• In NonlinearStateSpaceModel[eqns,] the Taylor linearization is with respect to the highest-order derivatives of about the point of the differential equations eqns.
• In computations where the operating point vi0 is Automatic, it is usually assumed to be zero.
• The following option can be given:
• NonlinearStateSpaceModel can be used in functions such as OutputResponse and SystemsModelSeriesConnect.

# Examples

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## Basic Examples(1)

Define the nonlinear system with output :

 In:= Out= Plot its response to a step input with initial states at the origin:

 In:= In:= Out= ## Properties & Relations(3)

Introduced in 2014
(10.0)