A method to control an internal combustion engine provided with an exhaust system for the exhaust gases of a motor vehicle having an exhaust duct and an exhaust gas after-treatment system comprising at least one catalytic converter (15, 17) arranged along the exhaust duct; and an oxygen sensor (18, 18*, 18**), preferably a linear one, to detect the air/fuel ratio of the exhaust gases providing an output that indicates the content of oxygen in the exhaust gases; and a burner, which is suited to introduce exhaust gases into the exhaust duct so as to speed up the heating of said at least one catalytic converter (15, 17), wherein inside the burner there is defined a combustion chamber, which receives fresh air through an air feeding device, which is provided with a pumping device feeding air, and fuel from an injector, which is designed to inject fuel into the combustion chamber, and a spark plug coupled to the burner so as to ignite the mixture present inside the combustion chamber; the method comprises the following steps: calculating a thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17) obtained with an objective value (λ OBJ) of the air/fuel ratio; and determining both an objective fuel flow rate (ṁ F_OBJ) and an objective air flow rate (ṁ A_OBJ) to be fed to the burner in order to obtain the thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17); the method is characterized in comprising the further step of: determining a nominal number (N NOM) of revolutions with which to operate the pumping device depending on the objective air flow rate (ṁ A_OBJ), on an ambient pressure (P ATM), on an ambient temperature (T ATM) and on an objective pressure (P A_OBJ) of the air flowing into a shut-off valve that regulates a duct located downstream of the pumping device; determining a closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device by means of a first PID controller, which tries to zero a difference between an objective value (λ OBJ) of the air/fuel ratio and an actual value (λ) of the air/fuel ratio measured by the oxygen sensor (18, 18*, 18**); determining a further contribution (N ADAT) of the number of revolutions with which to operate the pumping device depending on the integral action of the PID controller under stationary conditions; determining an actual number of revolutions with which to operate the pumping device by means of the sum of the nominal number (N NOM) of revolutions, of the closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device and of the further contribution (N ADAT) of the number of revolutions with which to operate the pumping device. calculating a thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17) obtained with an objective value (λ OBJ) of the air/fuel ratio; and determining both an objective fuel flow rate (ṁ F_OBJ) and an objective air flow rate (ṁ A_OBJ) to be fed to the burner in order to obtain the thermal power (P OBJ) needed to reach the nominal operating temperature of said at least one catalytic converter (15, 17); the method is characterized in comprising the further step of: determining a nominal number (N NOM) of revolutions with which to operate the pumping device depending on the objective air flow rate (ṁ A_OBJ), on an ambient pressure (P ATM), on an ambient temperature (T ATM) and on an objective pressure (P A_OBJ) of the air flowing into a shut-off valve that regulates a duct located downstream of the pumping device; determining a closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device by means of a first PID controller, which tries to zero a difference between an objective value (λ OBJ) of the air/fuel ratio and an actual value (λ) of the air/fuel ratio measured by the oxygen sensor (18, 18*, 18**); determining a further contribution (N ADAT) of the number of revolutions with which to operate the pumping device depending on the integral action of the PID controller under stationary conditions; determining an actual number of revolutions with which to operate the pumping device by means of the sum of the nominal number (N NOM) of revolutions, of the closed-loop contribution (N CL) of the number of revolutions with which to operate the pumping device and of the further contribution (N ADAT) of the number of revolutions with which to operate the pumping device.