How to write code for hankle and toeplitz matrix?

I have matrices like

F = [CA;CA^2;CA^3;CA^4;CA^5;CA^6;CA^7;CA^8;CA^9;CA^10]

and other matrix is

phi=[CB    0     0     0;
     CAB   CB    0     0;
     CA^2B CAB   CB    0;
     CA^3B CA^2B CAB   CB;
     CA^4B CA^3B CA^2B CAB;
     CA^5B CA^4B CA^3B CA^2B;
     CA^6B CA^5B CA^4B CA^3B;
     CA^7B CA^6B CA^5B CA^4B;
     CA^8B CA^7B CA^6B CA^5B;
     CA^9B CA^8B CA^7B CA^6B]

How can I do matlab coding for these matrices

[the cyclist]

I assume A, B, and C variables you already have.

[Matt J]

Does CA^2 signify C*A^2 or (CA)^2 where 'CA' is the name of one variable. Are A,B,C scalars are matrices and, if matrices, of what size?

[baruch]

I have matrices like

F = [CA;CA^2;CA^3;CA^4;CA^5;CA^6;CA^7;CA^8;CA^9;CA^10] and other matrix is

phi=[CB 0 0 0; CAB CB 0 0; CA^2B CAB CB 0; CA^3B CA^2B CAB CB; CA^4B CA^3B CA^2B CAB; CA^5B CA^4B CA^3B CA^2B; CA^6B CA^5B CA^4B CA^3B; CA^7B CA^6B CA^5B CA^4B; CA^8B CA^7B CA^6B CA^5B; CA^9B CA^8B CA^7B CA^6B]

How can I do matlab coding for these matrices if C=[0,0,0,0,0,1];

A=[0.951229424500714,0,0,0,0,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,0;-0.00799415471554044,2.05514658489028,0.951087777342890,0,0,0;0,0,0,1,0,0;3.85664115847093e-05,-0.00999690651487826,-5.08357475891134e-08,0.0100000000000000,1,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,1]

B=[0;0.00150727991601721;289.187620200957;0;-5.05813015832678e-06;0.00150727991601721]

I need generalised code as in case given above it is for N=10.if I take any value then what will be it's code?

Answer 1

[Roger Stafford]

My apologies! I was not thinking clearly when I wrote the nonsensical A.^(0:9). The following should produce the desired two arrays.

   M = 6;  % A is M x M, B is M x 1, C is 1 x M
   N = 10;
   F = zeros(N+1,M);
   F(1,:) = C;
   for k = 2:N+1
     F(k,:) = F(k-1,:)*A;
   end
   r = F(1:N,:)*B;
   c = [C*B;zeros(M-1,1)];
   phi = toeplitz(r,c);
   F = F(2:N+1,:);

[baruch]

phi=[CB 0 0 0; CAB CB 0 0; CA^2B CAB CB 0; CA^3B CA^2B CAB CB; CA^4B CA^3B CA^2B CAB; CA^5B CA^4B CA^3B CA^2B; CA^6B CA^5B CA^4B CA^3B; CA^7B CA^6B CA^5B CA^4B; CA^8B CA^7B CA^6B CA^5B; CA^9B CA^8B CA^7B CA^6B]

How can I do matlab coding for these matrices if C=[0,0,0,0,0,1];

A=[0.951229424500714,0,0,0,0,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,0;-0.00799415471554044,2.05514658489028,0.951087777342890,0,0,0;0,0,0,1,0,0;3.85664115847093e-05,-0.00999690651487826,-5.08357475891134e-08,0.0100000000000000,1,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,1]

B=[0;0.00150727991601721;289.187620200957;0;-5.05813015832678e-06;0.00150727991601721]

I need generalised code as in case given above it is for N=10.if I take any value then what will be it's code?

[Roger Stafford]

Isn't that what I have given you in the code above?

[baruch]

exactly sir.Thankyou.Sir have you worked on predictive control i am doing research work on that and want guideline

[Roger Stafford]

No, I am sorry. I have never worked in that area.

[baruch]

if you have any idea about any person who is expert in this area? I am searching but didn't find

Answer 2

[the cyclist]

F = C*A.^(1:10)

[baruch]

I have matrices like

F = [CA;CA^2;CA^3;CA^4;CA^5;CA^6;CA^7;CA^8;CA^9;CA^10] and other matrix is

phi=[CB 0 0 0; CAB CB 0 0; CA^2B CAB CB 0; CA^3B CA^2B CAB CB; CA^4B CA^3B CA^2B CAB; CA^5B CA^4B CA^3B CA^2B; CA^6B CA^5B CA^4B CA^3B; CA^7B CA^6B CA^5B CA^4B; CA^8B CA^7B CA^6B CA^5B; CA^9B CA^8B CA^7B CA^6B]

How can I do matlab coding for these matrices if C=[0,0,0,0,0,1];

A=[0.951229424500714,0,0,0,0,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,0;-0.00799415471554044,2.05514658489028,0.951087777342890,0,0,0;0,0,0,1,0,0;3.85664115847093e-05,-0.00999690651487826,-5.08357475891134e-08,0.0100000000000000,1,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,1]

B=[0;0.00150727991601721;289.187620200957;0;-5.05813015832678e-06;0.00150727991601721]

I need generalised code as in case given above it is for N=10.if I take any value then what will be it's code?

Answer 3

[Roger Stafford]

   phi = toeplitz(C*A.^(0:9)*B,zeros(1,4));

It is assumed that C*A^n*B is a scalar.

[baruch]

I have matrices like

F = [CA;CA^2;CA^3;CA^4;CA^5;CA^6;CA^7;CA^8;CA^9;CA^10] and other matrix is

phi=[CB 0 0 0; CAB CB 0 0; CA^2B CAB CB 0; CA^3B CA^2B CAB CB; CA^4B CA^3B CA^2B CAB; CA^5B CA^4B CA^3B CA^2B; CA^6B CA^5B CA^4B CA^3B; CA^7B CA^6B CA^5B CA^4B; CA^8B CA^7B CA^6B CA^5B; CA^9B CA^8B CA^7B CA^6B]

How can I do matlab coding for these matrices if C=[0,0,0,0,0,1];

A=[0.951229424500714,0,0,0,0,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,0;-0.00799415471554044,2.05514658489028,0.951087777342890,0,0,0;0,0,0,1,0,0;3.85664115847093e-05,-0.00999690651487826,-5.08357475891134e-08,0.0100000000000000,1,0;-0.00764874141234696,0.999384908699207,1.00818092264771e-05,0,0,1]

B=[0;0.00150727991601721;289.187620200957;0;-5.05813015832678e-06;0.00150727991601721]

I need generalised code as in case given above it is for N=10.if I take any value then what will be it's code?