Download presentation

Presentation is loading. Please wait.

Published byJulianna Paul Modified over 2 years ago

1
Linear Matrix Inequalities in System and Control Theory Solmaz Sajjadi Kia Adviser: Prof. Jabbari System, Dynamics and Control Seminar UCI, MAE Dept. April 14, 2008

2
Linear Matrix Inequality (LMI) Set of n polynomial inequalities in x, e.g., Convex constraint on x

3
Matrices as Variable Multiple LMIs

4
LMI Problems Feasibility Minimization Problem

5
How do we cast our control problems in LMI form? We rely on quadratic function V(x)=x’Px Three Useful Properties to Cast Problems in Convex LMI From Congruent Transformation S-Procedure Schur Complement

6
Congruent transformation

7
Stable State Feedback Synthesis Problem

8
S Procedure Three Useful Properties to Cast Problems in Convex LMI From Congruent Transformation S-Procedure Schur Complement

9
Reachable Set/Invariant Set for Peak Bound Disturbance The reachable set (from zero): is the set of points the state vector can reach with zero initial condition, given some limitations on the disturbance. The invariant set: is the set that the state vector does not leave once it is inside of it, again given some limits on the disturbance.

10
Reachable Set/Invariant Set for Peak Bound Disturbance Ellipsoidal Estimate Peak Bound Disturbance

11
Linear (thus convex) Verses Nonlinear Convex inequality Nonlinear (convex) inequalities are converted to LMI form using Schur Complement Three Useful Properties to Cast Problems in Convex LMI From Congruent Transformation S-Procedure Schur Complement

12
H ∞ or L 2 Gain

13
Norm of a vector in an ellipsoid Find Max of ||u||=||Kx|| for x in {x| x T Px≤c 2 }

15
A Saturation Problem Problem: Synthesis/Analysis of a Bounded State Feedback Controller (||u||__
{
"@context": "http://schema.org",
"@type": "ImageObject",
"contentUrl": "http://images.slideplayer.com/14/4239437/slides/slide_15.jpg",
"name": "A Saturation Problem Problem: Synthesis/Analysis of a Bounded State Feedback Controller (||u||
__

16
x T Px

17
x T Px

19
Good Reference Prof. Jabbari’s Note on LMIs S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, “Linear Matrix Inequalities in Systems and Control Theory”

Similar presentations

OK

Stability Region Analysis using composite Lyapunov functions and bilinear SOS programming Support from AFOSR FA9550-05-1-0266, April 05-November 06 Authors.

Stability Region Analysis using composite Lyapunov functions and bilinear SOS programming Support from AFOSR FA9550-05-1-0266, April 05-November 06 Authors.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on pin diodes Technical seminar ppt on recent interactive voice response system Ppt on organic led Ppt on credit policy of a bank Download ppt on social problems in india Ppt on manufacturing planning and control Collaborative strategic reading ppt on ipad Ppt on regular expression in php Ppt on total internal reflection experiment History of film editing ppt on ipad