Disturbance decoupling of multi-input multi-output discrete-time nonlinear systems by static measurement feedback

Abstract

This paper addresses the disturbance decoupling problem (DDP) for nonlinear systems, extending the results for continuous-time systems into the discrete-time case. Sufficient conditions are given for the solvability of the problem. The notion of the rank of a one-form is used to find the static measurement feedback that solves the DDP whenever possible. Moreover, necessary and sufficient conditions are given for single-input single-output systems, as well as for multi-input multi-output systems under the additional assumption.

Disturbance decoupling by measurement feedback

“…In this paper, we extend the results of Kaldmäe and Kotta [2012b] for MIMO discrete-time systems 1 . However, the extension is not direct since we relax certain integrability conditions.…”

“…Lemma 1. Kaldmäe and Kotta [2012a] The subspace Ω may be computed as the limit of the following algorithm:…”

“…In Kaldmäe et al [2013], similar results as in Isidori et al [1981] were given for discrete-time systems (though, more general feedback was used), using algebraic approach (lattice theory), that is able to address also certain type of non-smooth systems. A more general feedback, where the state of the compensator is not a function of the state of the system, but can be chosen independently of it, was used in Xia and Moog [1999] and Kaldmäe and Kotta [2012b], where sufficient conditions for the solvability of the problem by dynamic measurement feedback were given for continuous-and discrete-time SISO systems, respectively. For static measurement feedback solutions see Pothin et al [2002] and Kaldmäe and Kotta [2012a].…”

“…A more general feedback, where the state of the compensator is not a function of the state of the system, but can be chosen independently of it, was used in Xia and Moog [1999] and Kaldmäe and Kotta [2012b], where sufficient conditions for the solvability of the problem by dynamic measurement feedback were given for continuous-and discrete-time SISO systems, respectively. For static measurement feedback solutions see Pothin et al [2002] and Kaldmäe and Kotta [2012a].…”