Input-output gain analysis of positive periodic systems

This paper investigates the input-output gains, including l(1)- and l(infinity)-gains and L-1- and L-infinity-gains, of discrete-time and continuous-time positive periodic systems. For the discrete-time case, the input-output gain can be characterized by linear inequalities. For the continuous-time case, the input-output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input-output gain conditions, we find the l(1)- (L-1-) gain of discrete-time (continuous-time) positive periodic systems is equivalent to the of l(infinity)- (L-infinity-) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.