On partially minimum-phase systems and disturbance decoupling with stability

Abstract

In this paper, we consider the problem of disturbance decoupling for a class of non-minimum phase nonlinear systems. Based on the notion of partially-minimum phaseness, we shall characterize all actions of disturbances which can be decoupled via a static state feedback while preserving stability of the internal residual dynamics. The proposed methodology is then extended to the sampled-data framework via multi-rate design to cope with the rising of the so-called sampling-zero dynamics intrinsically induced by classical single-rate sampling.

On stable right-inversion of non-minimum-phase systems

“…In this section, we extend the approach proposed in [11] for extracting the minimum-phase component of a general non-minimum phase systems (1). The approach is based on output factorization; namely, starting from (1), we identify a new dummy output y s (t) = C s x(t) corresponding to the stable component of the zero-dynamics associated to (1) and related to (1b) through the differential equation…”

“…The idea of employing factorization, properly introduced in [10] for studying the zero-dynamics of sampled-data systems, and consequently partial dynamic cancelation has been formalized and developed in [11] to deal with feedback linearization of nonlinear single-input single-output (SISO) non-minimum phase systems (i.e., whose zero-dynamics are unstable). The design approach represents a first generalization to the nonlinear context of the idea of assigning part of the eigenvalues over part of the zeros of the transfer function of a linear system (partial zero-pole cancelation).…”

“…Supported by Université Franco-Italienne/Università Italo-Francese (Vinci Grant 2019) and by Sapienza Università di Roma (Progetti di Ateneo 2018-Piccoli progetti RP11816436325B63). 1 In this paper, the results in [11] are extended to the multi-input multi-output context by providing a systematic procedure for extracting, via factorization, a dummy output identifying the minumum-phase component of a dynamical system. In particular, focusing on linear time-invariant and right-invertible dynamics, we show how the Smith form can be suitably exploited for factorizing the matrix transfer function and extract, in the state-space representation, the output identifying the minimum-phase component of the original system.…”