Home > mpt > extras > control > mpt_getStabFeedback.m

# mpt_getStabFeedback

## PURPOSE

MPT_GETSTABFEEDBACK Computes a stabilizing feedback law for a PWA system

## SYNOPSIS

function [F,P,feasible] = mpt_getStabFeedback(A,B,Q1,R,Options)

## DESCRIPTION

```MPT_GETSTABFEEDBACK Computes a stabilizing feedback law for a PWA system

[F,P,feasible] = mpt_getStabFeedback(A,B,Q,R)

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DESCRIPTION
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Function computes a stabilizing feedback law for a PWA system defined by the
cells A{}, B{}. It is assumed that the dynamics are valid in the entire state-
space. The obtained feedback law also minimizes the cost J=x'Q1x + u'Ru.
Computation solves an SDP (Yalmip required).

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INPUT
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A{},B{}          - cell array defining the dynamics; x^+=A{i}x+B{i}u
Q,R              - cost objective J=x'Qx + u'Ru.
Options.verbose  - level of verbosity

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OUTPUT
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F{}       - cell array containing the feedback law for each dynamic i
P         - common quadratic Lyapunov function V(x)=x'Px for feedback laws F{}
feasible  - 0/1 flag. Set to 1 if computation was successful

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• set SET Set a field of MPTCTRL objects
• double DOUBLE Function used to access internal properties of the given polytope
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array
• set SET Used to modify internal properties of a given polytope object
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• mpt_getCommonLyapFct MPT_GETCOMMONLYAPFCT Computes common Lyapunov function for PWA system
This function is called by:
• mpt_computePWATset MPT_COMPUTEPWATSET Computes a stabilizing control invariant set (+ controllers) around the origin
• mpt_dlqr MPT_DLQR Linear-quadratic regulator design for discrete-time systems.

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