Global stabilization of feedforward nonlinear time-delay systems by bounded controls

Lam³

2018

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%

“…Remark Similar to the analysis in our previous work, the linear terms A x i ( t − h i ) (defined by

L_{i} false(x_{t} false)

), i ∈ I [2, p + 1], in can be replaced by the following general ones:

{scriptL}_{i} (x_{t}) = \sum_{j = i}^{p + 1} \sum_{k = 1}^{m_{i j}} A_{i j k} x_{j} (t - h_{i j k}), i \in I [2, p + 1],

where m i j ≥ 1 are integers, h i j k are known nonnegative numbers, and

A_{i j k} \in R^{2 \times 2}

are some known matrices such that the linearized system of is controllable.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Lam³

2018

Self Cite

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

2018

Self Cite

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.

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

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.