Average passivity for discrete-time and sampled-data linear systems

Average passivity concepts are proposed for linear time-invariant discrete-time as well as sampled-data dynamics to remove the direct input-output link obstacle. Necessary and sufficient conditions for average passivity are given in terms of LMI´s. Direct discrete-time stabilizing and damping control strategies are proposed for average passive systems or Lyapunov stable dynamics. Linear port-controlled Hamiltonian - PCH systems are treated as an example to illustrate the stabilizing and damping performances through a simulated example.