A detailed theoretical analysis of stability in a quantum dash distributed Bragg reflector (DBR) laser is presented under the small-signal condition. The influence of p-type doping and inhomogeneous line broadening on the hysteresis width of the quantum dash DBR laser is studied using a rate equation model that includes all of the multidiscrete energy levels in the valence and conduction bands. Our calculations show that a large hysteresis width is obtained by detuning the laser by ~10 meV above the ground state energy and doping the dashes by acceptor concentration NA=3.7×1017 cm-3. Also we find that a large self-pulsation frequency is obtained by detuning the laser by -15 meV from the ground state energy and doping the dashes by NA=2.5×1017 cm-3. The laser hysteresis width can be greatly reduced by doping the dashes with NA>1×1018 cm-3.