Disturbance Decoupling for Nonlinear Time‐delay Systems

Abstract

The disturbance decoupling problem is studied for a general class of nonlinear systems with multiple delays. Necessary and sufficient conditions are given for the solvability of the problem, in geometric terms involving so‐called controlled invariant modules. An example is included which shows that there is no unique “standard” solution to disturbance decoupling in opposition to the well known situation of systems without delays.

Disturbance Decoupling of Time Delay Systems

“…Nevertheless, the conditions of theorem 1 in [7] are not satisfied. Nevertheless, the conditions of theorem 1 in [7] are not satisfied.…”

“…This system is disturbance decoupled, since the submodule Ω = span ( ] {dx 1 (t)} is invariant. Nevertheless, the conditions of theorem 1 in [7] are not satisfied. Really, if…”

Stability issues in disturbance decoupling for switching linear systems

“…Disturbance decoupling, which is a main issue in control system design, was first solved for linear systems in the late sixties, within the geometric approach (see, e.g., [1,2] and the references therein). Since then, the problem has been reformulated for different classes of dynamical systems and, due to the peculiarities of each context, it still attracts a fair amount of research effort: e.g., nonlinear systems have recently been considered in [3], descriptor systems and systems over rings in [4], timedelay systems in [5], linear parameter varying systems in [6,7].…”

“…Disturbance decoupling, which is a main issue in control system design, was first solved for linear systems in the late sixties, within the geometric approach (see, e.g., [1,2] and the references therein). Since then, the problem has been reformulated for different classes of dynamical systems and, due to the peculiarities of each context, it still attracts a fair amount of research effort: e.g., nonlinear systems have recently been considered in [3], descriptor systems and systems over rings in [4], timedelay systems in [5], linear parameter varying systems in [6,7].Lately, disturbance decoupling has been tackled for switching linear systems, that are dynamical systems described by a set of linear time-invariant systemseach of them modeling a different mode of operationand a switching signal, designating the active mode at each time instant [8][9][10]. Indeed, when switching linear systems are involved, the problem of disturbance decoupling lends itself to a number of formulations, character-…”

Disturbance Decoupling With Stability in Discrete-Time Switching Linear Systems: Arbitrary Switching

“…Disturbance decoupling has been studied for various other classes of dynamical systems and, because of the peculiarities arising in each context, it still attracts the interest of the research community. Indeed, disturbance decoupling has recently been considered for nonlinear systems [7], descriptor systems and systems over rings [8], time-delay systems [9,10], linear parameter varying systems [11,12], hybrid linear systems with state jumps [13,14], and switching linear systems [15,16,17,18,19,20,21,22,23,24,25,26,27]. The motivation for investigating possible solutions of the disturbance decoupling problem for more general classes of dynamical systems than linear time-invariant systems is not only the intrinsic theoretic interest of finding relaxed solvability conditions, but also the need to find powerful tools to solve more intricate problems like, for instance, model matching [28,29,30,31].…”