Feedback passivity of nonlinear discrete-time systems with direct input–output link

Abstract

This paper is devoted to the study of the feedback passivity property in nonlinear discrete-time systems. The relative degree and zero dynamics of the non-passive system are related to the feedback passivity of the system. Two main results are presented. First, some relative degreerelated properties of passive systems in general form are stated. Second, sufficient conditions in order to render a multiple-input multiple-output (MIMO) system passive by means of a static state feedback control law are obtained.

Lyapunov stabilization of discrete-time feedforward dynamics

“…Although important works bridge the gap between the continuous-time and discrete-time domains through different methodologies (e. g., [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]), hard difficulties represent an obstacle in extending results that are well-known and elegant in continuous time. Those issues are essentially concerned with the generic nonlinearity in the control variable of the dynamics and the difficulty to settle the geometric structure underlying its evolutions.…”

A Speed-Gradient-Based Method to Passify Nonlinear Discrete-Time Systems

“…In these works, the feedback passivity problem is based on the properties of the relative degree and zero dynamics of the non-passive system and the approach is inherited from the continuous-time case (Byrnes et al, 1991). These results have been recently extended in (Navarro-López and Fossas-Colet, 2004) to general systems without requiring V ( f (x, u)) to be quadratic in u. The feedback dissipativity property is treated for single-input single-output (SISO) nonlinear discrete-time systems of general form in (NavarroLópez, 2002;.…”

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

“…Even though input-output stability conditions can be stated in a general Hilbert spacethat is, they are valid for L 2 and ℓ 2 -dissipativity conditions in the state space realization are very different in the continuous-time and discrete-time settings; in the same way that Lyapunov-type stability conditions or Riccati equation are different. For example, passive discrete systems require a direct input-output link [11,28,29,30,31,35]. For the case of linear systems this means that D = 0.…”

“…Recently, the results of Navarro-López given in [28,31,30] have been further expanded to discrete-time periodically controlled systems [39] and nonlinear discrete-time switched systems [38].…”

“…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].…”