Stability of delayed feedback controllers for discrete time systems

IFAC Proceedings Volumes

2012

In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a nonlinear feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. By restricting the gain matrix to a special form we obtain some novel stability results. The stability proofs also give the possible feedback gains which achieve stabilization. We also present some simulation results.

Section: Introductionmentioning

confidence: 76%

“…Although the subject is still open and deserves further investigation, we note that the limitation of DFC stated above holds for discrete time case, see e.g. (Ushio, 1996), (Morgül, 2003), (Morgül, 2005a).…”

Section: Introductionmentioning

confidence: 98%

A Nonlinear Control Scheme for Discrete Time Chaotic Systems

IFAC Proceedings Volumes

2012

“…It can be shown that Σ T cannot be stabilized with this scheme if [Ushio, 1996;Morgül, 2003a], and a similar condition can be generalized to the case n > 1 [Hino et al, 2002]. A set of necessary and sufficient conditions to guarantee exponential stabilization for n = 1 and n ≥ 1 can be found in [Morgül, 2003a] and [Morgül, 2005a], respectively.…”

Section: Problem Statementmentioning

confidence: 97%

“…This modification, which is also used in [Morgül, 2003a[Morgül, , 2005a[Morgül, , 2005b, does not change the generality of the results. Note that the DPDFC scheme given by (12) and (13) achieves only local stabilization, i.e.…”

Section: A Simple Implementationmentioning

confidence: 99%

See 1 more Smart Citation

On the Stabilization of Periodic Orbits for Discrete Time Chaotic Systems by Using Scalar Feedback

Int. J. Bifurcation Chaos

2007

In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems by using a scalar input. We use a simple periodic delayed feedback law and present some stability results. These results show that all hyperbolic periodic orbits as well as some nonhyperbolic periodic orbits can be stabilized with the proposed method by using a scalar input, provided that some controllability or observability conditions are satisfied. The stability proofs also lead to the possible feedback gains which achieve stabilization. We will present some simulation results as well.

Further stability results for a generalization of delayed feedback control

2012

Nonlinear Dyn

In this paper, we consider the stabilization of unstable periodic orbits for one-dimensional and discrete time chaotic systems. Various control schemes for this problem are available and we consider a recent generalization of delayed control scheme. We prove that if a certain condition, which depends only on the period number, is satisfied then the stabilization is always possible. We will also present some simulation results. © Springer Science+Business Media B.V. 2012