Why redeclaring the same condition when soving for a set of constraints gives infeasible Problem

[Rayane BENYOUCEF]

Hi everyone,

I am solving for eight constraints (code attached), basically, all of them have some condtions in common, when I solve  each alone I get the LMI seccessfully solved,  when I solve for all of them I get infeasible problem but when I remove some conditions in one of the constraints and solve for the whole of them, I don't get infeasible problem although these same deleted conditions are declared in all of the previous constraints.

Any ideas WHY!! 

Thank you in advance.

[Johan Löfberg]

I cannot reproduce infeasibility in the code you sent. Both problems are solved succesfully (sdpt3)

BTW, you should improve readability of your code significantly by using loops and placing data/variables in cells/nd-arrays. Also, 'full' is redundant for non-square matrices, and 'symmetric' is redundant for square matrices

[Rayane BENYOUCEF]

Hey Johan

I took in consideration what you invoked in your answer. But problem still persisting, well I realized that I did a small mistake in my previous code. Here what I want to solve:

taken from: 'Observer-Based Control of Discrete-Time LPV Systems With Uncertain Parameters, W. P. Maurice H. Heemels, Jamal Daafouz, and Gilles Millerioux'

I verified all the conditions before applying this theorem. everything is good I even did some simple code (simpleCode.m attached) to make sure everything is OK and the observer works pretty much fine.

Yet I still have infeasible problem in my code (code.m attached)

Please any help will be appreciated

[Johan Löfberg]

already this is infeasible so why even bother trying to debug with 7 more sytems (i.e. already for once single dynamics)

i = 1;

j = 1;

M1=[G1{:,i}'+G1{:,i}-P1i{:,j}, zeros(3),G1{:,i}*Aa1{:,i}-F1{:,i}*C,G1{:,i}; 

    zeros(3), eye(3), eye(3), zeros(3); Aa1{:,i}'*G1{:,i}'-C'*F1{:,i}', eye(3), P1i{:,i}, zeros(3);

    G1{:,i}', zeros(3), zeros(3),sig1*eye(3)];

constraints11= [constraints11, M1>0];    

globalConstraints=[globalConstraints, -P1i{:,i}<0];

globalConstraints=[globalConstraints , sig1>=1];

%%%%%%%%%%%%%%%%%%%%%%constraints1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

constraints1=[constraints11,globalConstraints];

optimize(constraints1)

In this model, you cannot replace sig>0 with sig>=1. THe model i not homogenuous. Still, sig>=0 also leads to infeasibility

and P1i>=0 is redundant as you already have that matrix in the diagonal of the large LMI (in the same sense that sig>0 is redundant as you have sig*I in the diagonal )

[Rayane BENYOUCEF]

I trired to sove the LMIs with i =1 and j=1. I even tried with i=1 and j=1:8 when sig1>=1 and  also sig1>0 I got them all successfully solved using (SeDuMi-1.3) solver. the problem was when I solve them all together at once.

Please I need a reply or even a suggetion. THANKS

[Johan Löfberg]

Well, the problem is simply not feasible, so nothing special to do or say.