Global Stabilization of the Multiple Integrators System by Delayed and Bounded Controls

Zhou, Bin; Yang, Xuefei

doi:10.1109/tac.2015.2513371

Cited by 32 publications

(24 citation statements)

References 24 publications

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“…Remark Compared with our previous results in the works of Zhou and Yang and Yang et al, the novelty of Theorem can be summarized as follows. (i) The nature of the oscillators is significantly different from that of chains of integrators.…”

Section: Resultsmentioning

confidence: 87%

“…(i) The nature of the oscillators is significantly different from that of chains of integrators. Thus, the new special canonical form of the considered system (see ) we constructed is different from those in the work of Zhou and Yang . Moreover, in order to guarantee the asymptotic stability of the closed‐loop system in the linear region, a different method from is adopted.…”

Section: Resultsmentioning

confidence: 99%

“…Thus, the new special canonical form of the considered system (see ) we constructed is different from those in the work of Zhou and Yang . Moreover, in order to guarantee the asymptotic stability of the closed‐loop system in the linear region, a different method from is adopted. (ii) The nonlinear controllers proposed in the work of Yang et al consist of nested saturation functions, whereas controllers in this paper consist of cascade saturation functions.…”

Section: Resultsmentioning

confidence: 99%

“…(ii) The nonlinear controllers proposed in the work of Yang et al consist of nested saturation functions, whereas controllers in this paper consist of cascade saturation functions. (iii) The controllers in the work of Zhou and Yang and Yang et al are based on energy function analysis (see), whereas controllers are based on the Lyapunov function analysis. (iv) The linear system in contains not only the current states but also the delayed states, whereas the systems in the works of Zhou and Yang and Yang et al do not contain delayed states.…”

Section: Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

Yang

Zhou

Lam³

2018

Intl J Robust & Nonlinear

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Summary For the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.

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Section: Resultsmentioning

confidence: 87%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

Yang

Zhou

Lam³

2018

Intl J Robust & Nonlinear

Self Cite

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“…The differences between the proposed method and the existing ones are stated as follows. Compared with , the chain of integrators with higher‐order nonlinear terms is investigated with the aid of the technique of assigning small saturation levels to attenuate nonlinearities. Compared with , the stability analysis is simplified to some extent and the less conservative estimates on the allowed delay will be obtained. More specifically, by using the state transformation of , the saturation reduction analysis can be carried out in a cancellation way.…”

Section: Introductionmentioning

confidence: 99%

New Saturated Delayed Control for a Chain of Integrators with Nonlinear Terms

Kang

et al. 2017

Asian Journal of Control

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This paper investigates the saturated delayed stabilization of a chain of integrators with higher‐order nonlinear terms. With the aid of a recent state transformation, the system is transformed into a canonical form in which time delay appears in both input and states. As a result, natural cancellations can be fully used in the saturation reduction analysis, and fewer terms need to be estimated in the asymptotical stability analysis of the reduced system. In addition, a single tuneable parameter is introduced to the special state transformation, which facilitates compensating an arbitrarily large input‐delay. As an example, a simplified inertia wheel pendulum system is provided with an explicit controller and numerical simulations are given to demonstrate the effectiveness of the suggested controller.

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Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

Yang

Zhou

2018

Intl J Robust & Nonlinear

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This paper studies the problem of global stabilization of a family of discrete-time feedforward time-delay systems with bounded controls. Two classes of nonlinear control laws are established based on a special canonical form of the considered system. The proposed control laws use not only the current states but also the delayed states for feedback and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed-loop system significantly. A practical example is given for illustration.

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Global Stabilization of the Multiple Integrators System by Delayed and Bounded Controls

Cited by 32 publications

References 24 publications

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

New Saturated Delayed Control for a Chain of Integrators with Nonlinear Terms

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

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