a11 = -0.4;
a12 = -0.8;
a21 = 1;
a22 = -0.3;

b1 = -1.4;
b2 = 0.08;

c = 0.9;
d = 0.0086;
T = 0.12;

A = [
    a11 a12  b1;
    a21 a22  b2;
    0   0   -1/T
    ];

B = [
    0; 0; 1/T
    ];

syms omega_z(t) alpha(t) delta(t) u(t) n_y(t)

assume(t, "real")

n_y = c * alpha + d * delta;

X = [omega_z; alpha; delta];
X_star = [omega_z; n_y; delta];

% Получим матрицу T
% Матрица Т состоит из нулей кроме 3-х элементов: t_11 = 1; t_22 = 1/c;
% t_23 = -d/c

matrix_T = [
            1   0    0;
            0 1/c -d/c;
            0   0    1
            ];

% X == matrix_T * X_star

Уравнение в изначальном виде:
dX = diff(X, t);
dX_star = diff(X_star, t);

eq1 = dX == A*X + B*u;
Уравнение при переходе к новому базису:
A_star = inv(matrix_T)*A*T
B_star = inv(matrix_T)*B
% dX_star == A_star * X_star + B_star * u
tmp = @(t, omega_z, n_y, delta) A_star * X_star + B_star * u




tspan = [0 3];
y0 = -5:5;
tmp1 = ode45(tmp, tspan, y0)
plot(t, tmp1(:, 2), '-.')

% A = 1;
% B = 2;
% tspan = [0 5];
% y0 = [0 0.01];
% [t,y] = ode45(@(t,y) odefcn(t,y,A,B), tspan, y0);
%
% plot(t, y(:,1), '-o', t, y(:,2), '-.')
tmp;

function dydt = odefunc(t, exp)
    dydt = zeros(3, 1);
    dydt(1) = 1;
end


function dydt = odefcn(t,y,A,B)
  dydt = zeros(2,1);
  dydt(1) = y(2);
  dydt(2) = (A/B)*t.*y(1);
end