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

Self Cite

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.

Section: A Novel State‐space Transformationmentioning

confidence: 80%

Section: A Novel State‐space Transformationmentioning

confidence: 80%

“…Then, similar to (27), the derivative of V p−1 ( p−1 ) along the trajectories of system (31) satisfieṡ…”

Section: Nonlinear Time-delay Systems With Identical Oscillatorsmentioning

confidence: 99%

Section: A Novel State‐space Transformationmentioning

confidence: 99%

Section: Introductionmentioning

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

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Bounded control of feedforward nonlinear systems subject to input time‐delay

Yang

Zhou

Lam³

et al. 2020

SummaryThis article is concerned with the global stabilization problem of a family of feedforward nonlinear time‐delay systems whose linearized system consists of multiple distinct oscillators. To fully utilize the delayed information and maintain the state decoupling property in the controller design, the considered nonlinear feedforward system is first transformed into a new system which contains time delays in both its input and states based on a novel model transformation containing time delays, and then the stabilizing saturated controller for the transformed system is designed based on the recursive design method. Meanwhile, explicit stability conditions are also provided. When the linearized system is a cascade of multiple oscillators and multiple integrators, a modified saturated feedback control utilizing not only the current state but also the delayed state is also established for the corresponding global stabilization problem. Two examples, including a practical one, are given to show the effectiveness and superiority of the proposed approaches.

Output‐feedback stabilization of a class of stochastic high‐order nonlinear systems with stochastic inverse dynamics and multidelay

Hui

Zhu

2021

In this article, the problem of output-feedback stabilization for a class of stochastic high-order nonlinear systems with stochastic inverse dynamics and multidelay is studied. In the control scheme, an output-feedback controller with a reduced-order observer is designed to globally stabilize the whole system. Different from the classical literature on stochastic upper-triangular systems, a high-gain-based technique is utilized to eliminate the effect of uncertainties in z 0 -subsystem. By skillfully choosing suitable forms of the control gains and the Lyapunov-Krasovskii functional, we analyze the global asymptotic stability in probability of the closed-loop system. Finally, two simulation examples are presented to show the effectiveness of our theoretical results.