In muscle, Phosphorylase a is inactivated by
In the liver, the role of glycogen is to provide free glucose for export to maintain the blood concentration of glucose. 
In muscle the role of glycogen is to provide a source of glucose-6-phosphate for glycolysis in response to the need for ATP for muscle contraction.
In both tissues, the enzyme is activated by phosphorylation catalyzed by phosphorylase kinase (to yield phosphorylase a) and inactivated by dephosphorylation catalyzed by phosphoprotein phosphatase (to yield phosphorylase b), in response to hormonal and other signals.
There is instantaneous overriding of this hormonal control. Active phosphorylase a in both tissues is allosterically inhibited by ATP and glucose-6-phosphate; in liver, but not muscle, free glucose is also an inhibitor.​

Harper 30th edition page 179
cAMP
Ca2+ ion
Glucose
ATP