/* sdpsol source for the LQR design example:
 *
 * min \int_0^\inf (y^Ty + u^2)
 * where  \dot{x} = [0,1;-1,0]x + [0;1]u  (system)
 *        y = [3,1]x                      (system)
 *        u = Kx                          (control)
 *
 * see p.114 of "Linear Matrix Inequalities in System
 * and Control Theory" by Boyd et al. for details
 */

A = [0,1;-1,0];
B = [0;1];
C = [3,1];

variable Q(2,2) symmetric;  /* Q = P^{-1} */
variable Y(1,2);            /* Y = KQ */
variable t;

 [A*Q+Q*A'+B*Y+Y'*B', Q*C', Y';
  C*Q,               -1,    0;
  Y,                  0,   -1 ] < 0;
 Q > t;
 t > 0;

maximize min_eig_Q = t;
