Control of chaos from a piecewise linear hysteresis circuit

Saito, Toshimichi; Mitsubori, Kunihiko

doi:10.1109/81.376872

Cited by 50 publications

(26 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…R,Ḡ l , and a set of positive scalars ε il jk >0 such that for all (i, j) ∈ , (l, k) ∈ˆ , the conditions (13)- (15) and the following LMIs are satisfied:…”

Section: Theorem 32mentioning

confidence: 99%

See 1 more Smart Citation

Delay‐dependent non‐synchronized robust ℋ_∞ state estimation for discrete‐time piecewise linear delay systems

Qiu

Feng

Yang

2009

Adaptive Control & Signal

View full text Add to dashboard Cite

This paper investigates the problem of delay-dependent robust H ∞ filtering design for a class of uncertain discrete-time piecewise linear state-delayed systems where state space instead of measurable output space partitions are assumed so that filter implementation may not be synchronized with plant state trajectory transitions. The state delay is assumed to be time-varying and of an interval-like type. The uncertainties are assumed to have a structured linear fractional form. The objective is to design a piecewise linear state estimator guaranteeing the asymptotic stability of the resulting filtering error system with robust H ∞ performance . Based on a new delay-dependent piecewise Lyapunov-Krasovskii functional combined with Finsler's Lemma, a novel delay-dependent robust H ∞ performance analysis result is first presented and the filter synthesis is then developed. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities, which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

show abstract

“…R,Ḡ l , and a set of positive scalars ε il jk >0 such that for all (i, j) ∈ , (l, k) ∈ˆ , the conditions (13)- (15) and the following LMIs are satisfied:…”

Section: Theorem 32mentioning

confidence: 99%

“…are encountered [10][11][12][13][14]. It is also known that many chaotic circuits can be described by piecewise linear systems [15]. Moreover, by using the approximation scheme, piecewise linear systems provide a powerful means to analysis and synthesis for many nonlinear control systems [16].…”

Section: Introductionmentioning

confidence: 99%

Delay‐dependent non‐synchronized robust ℋ_∞ state estimation for discrete‐time piecewise linear delay systems

Qiu

Feng

Yang

2009

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…It is also known that many chaotic circuits can be described by piecewise linear systems [8,9]. Moreover, by using the approximation scheme, piecewise linear systems provide a powerful means of analysis and synthesis for many nonlinear control systems [10].…”

Section: Introductionmentioning

confidence: 99%

Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems

Qiu

Feng

Gao

2010

J. Control Theory Appl.

View full text Add to dashboard Cite

This paper investigates the problem of robust H-infinity state estimation for a class of uncertain discretetime piecewise affine systems where state space instead of measurable output space partitions are assumed so that the filter implementation may not be synchronized with plant state trajectory transitions. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, two different approaches are developed to the robust filtering design for the underlying piecewise affine systems. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.

show abstract

“…Hartley and Mossayebi [IS] showed the control of modified Chua's circuit systems and demonstrated how to design a controller for tracking the capacitor voltage of the system. Saito and Mitsubori [14] proposed a simple control method to stabilize chaotic attractor to desired periodic orbit. Ramirez [15] presented a nonlinear feedback control to a chaotic system.…”

Section: Introductionmentioning

confidence: 99%

“…If given a desired state, say t-4 ret, -rrcl + .f'(~&, f(x&) to be tracked, then a proportional feedback k&,,, --X) is added to be the second feedback of controller II. If the input state is .r, then the controller II is If instead the input state is variable y then the second feedback of the controller 14 should be replaced by u2 = kp( yrrf -y). The block diagram of the control system is shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

A linear continuous feedback control of Chua's circuit

Hwang

Jin-Yuan²,

Rong-Syh

1997

Chaos, Solitons & Fractals

112

View full text Add to dashboard Cite

Abstract-A continuous feedback controller is designed to suppress and eliminate the chaotic behavior of Chua's circuit. This controller is constructed by the following two phases. First, the set of equilibrium points is extended by virtue of embedding suitable feedback terms in the control channel. Second, a state error term is then added to steer the dynamics of the control system to a fixed point or a limit cycle. The stability region of Chua's circuit with control is determined via the Routh-Hurwitz criterion. Some numerical simulations are given to demonstrate the effect of the control design. 0 1997 Elsevier Science Ltd

show abstract

Control of chaos from a piecewise linear hysteresis circuit

Cited by 50 publications

References 14 publications

Delay‐dependent non‐synchronized robust ℋ_∞ state estimation for discrete‐time piecewise linear delay systems

Delay‐dependent non‐synchronized robust ℋ_∞ state estimation for discrete‐time piecewise linear delay systems

Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems

A linear continuous feedback control of Chua's circuit

Contact Info

Product

Resources

About

Control of chaos from a piecewise linear hysteresis circuit

Cited by 50 publications

References 14 publications

Delay‐dependent non‐synchronized robust ℋ∞ state estimation for discrete‐time piecewise linear delay systems

Delay‐dependent non‐synchronized robust ℋ∞ state estimation for discrete‐time piecewise linear delay systems

Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems

A linear continuous feedback control of Chua's circuit

Contact Info

Product

Resources

About

Delay‐dependent non‐synchronized robust ℋ_∞ state estimation for discrete‐time piecewise linear delay systems

Delay‐dependent non‐synchronized robust ℋ_∞ state estimation for discrete‐time piecewise linear delay systems