# dynamicsClosedLoopLinearMeasErr

system dynamics for the closed-loop system controlled with the linear control law

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See Also
- References

## Syntax

f = dynamicsClosedLoopLinearMeasErr(t,x,w,nx,nu,dynamics)

## Description

This function implements the closed loop system dynamics for the case that the system is controlled by the linear control law. Thereby, the original system dynamics of the benchmark models are extended by auxiliary states that store the input zonotope, the states at the beginning of the time step, and the set of measurement errors. The implementation with auxiliary states guarantees that the control inputs are kept constant during one time step. Further, the value from the input zonotope (=control input) is insterted into the open-loop system dynamic of the benchmark modlel, which yields the equations for the closed-loop system.

## Input Arguments

x | system states x (dimension: [nx,1])
w | disturbances = input to the closed loop controlled systme (dimension: [nx,1])
p | parameter vector
nx | number of system states
nu | number of control inputs to the system
dynamics | function handle to the function implementing the open-loop dynamics of the system

## Output Arguments

f | value of the dynamic funcion = time derivative of x

## See Also

`convexInterpolationControl`, dynamcisClosedLoopExact

## References

- [1] Schuermann et al. (2017), Convex interpolation control with formal guarantees for disturbed and constrained nonlinear systems

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