In this note, a new technique is proposed for the global stability analysis of adaptive control of time-varying systems. The proposed method is based on the evaluation of possible burstings in the adaptive loop. Its simplicity and effectiveness is demonstrated by analyzing global stability and performance of the discrete-time direct adaptive controller. Developed technique reflects physical phenomena inside the adaptive loop, i.e., possible occurrence of instabilities and burstings. Precise upper bounds on the admissible speed of the parameter variations and on all the signals are established in terms of clearly defined physical quantities.