Generalized controlled invariance for discrete-time nonlinear systems with an application to the dynamic disturbance decoupling problem

Abstract

In analogy with the continuous-time case, a general notion of controlled invariance with respect to quasi-static-state feedback is introduced for discrete-time nonlinear systems which incorporates the earlier definition of controlled invariance with respect to regular static-state feedback. This new notion is used to derive a geometric solution to the dynamic disturbance decoupling problem. The proposed solution is a natural generalization of the geometric solution to the static disturbance decoupling problem.

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

“…Consider a subspace Ω k . By (2), Ω k+1 ⊂ Ω k or Ω k+1 = Ω k . Since the subspace Ω k is a finite-dimensional vector space, at certain step k * + 1, Ω k * = Ω k * +1 .…”

“…The disturbance decoupling problem (DDP) for a discrete-time nonlinear control system by state feedback has been addressed in many papers (see [2,3,7,8,14,16]). Most papers extend the results known for continuous-time systems into the discrete-time domain (e.g.…”

Geometric approach for observability and accessibility of discrete‐time non‐linear switched impulsive systems

“…Differential geometric approach has proved to be effective for the analysis and synthesis of non-linear control systems; see [20][21][22]. Significant attention focused on the control of non-linear systems based on the differential geometry theory, and the results have been used in various applications such as robots, power systems and aerospace vehicles.…”

Output Feedback Disturbance Decoupling in Discrete-Time Nonlinear Systems

“…The disturbance decoupling problem (DDP) for discretetime nonlinear control system by state feedback has been addressed in many papers: Aranda-Bricaire and Kotta [2004Kotta [ , 2001, Fliegner and Nijmeijer [1994], Grizzle [1985], Kotta and Nijmeijer [1991], Monaco and Normand-Cyrot [1984]. Most results extend the known results for continuous-time systems (see for example, Nijmeijer and van der Schaft [1990], Conte et al [2007], Isidori [1995]) and all these papers deal with the systems described by the difference equations defined in terms of sufficiently smooth functions.…”