Nonlinear average passivity and stabilizing controllers in discrete time

Lyapunov stabilization of discrete-time feedforward dynamics

“…u-average passivity and PBC design GAS of the equilibrium can now be achieved through uaverage passivity-based control as introduced in [14]. The following definitions are recalled.…”

“…Definition 3.1 (u-average passivity, [14]): The dynamics (13), with output y = H(x, u) is u-average passive with positive definite storage function S(·) if the following inequality holds for any u ∈ R…”

“…This latter notions enables to relax the necessity of a direct throughput as the usually required by passivity of discrete-time systems. At present, u-average passivity based controllers [14] control Lyapunov design at large) can be discussed along these lines as exploited in the present paper with reference to stabilization of cascade dynamics.…”

Towards -stability of discrete-time reset control systems via dissipativity theory

“…For the case of linear systems this means that D = 0. There is a growing effort to remove this direct input-output link restriction for either the linear or the nonlinear case [27,36]. Unlike discrete-time systems, continuous-time systems which are passive have a relative degree of one.…”

“…First, characterisation of passivity, dissipativity, and feedback passivity and dissipativity by using zero dynamics and relative degree properties [11,27,28,31,30,35]. Second, preservation of dissipativity and stability properties under sampling [26,24,25,32].…”