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

Abstract

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.

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

“…It follows from Assumption 1 that (t) in (16) and 1 (t) in (23) are unknown functions satisfying (t) ≤ 0 e 0 t and 1 (t) ≤ 01 e 01 t , respectively, in which 0 , 01 are unknown parameters and 0 , 01 are defined in (3). Moreover, d * , d in (1) are unknown parameters.…”

“…Then, we can obtain h 1 (t) ≥ 0 on t ∈ [t 1 , +∞). Similarly, there must exist the times t 2 , t 3 , (30), respectively. Thereafter, it can be verified that there must exist the time t 1 such that…”

“…It is well known that time delays are frequently encountered in various engineering fields such as chemical processes, rolling mills, and so on, which may cause the instability or performance degradation of the systems. [1][2][3] Furthermore, almost all physical systems are nonlinear in nature, and nonlinear time delay systems have uncontrollable linearization around the origin, so their stability/stabilization has been considered as one of the most challenging subjects. [4][5][6] In recent years, many stability results have been obtained from various perspectives (see .…”

Realizations in feedforward forms of nonlinear input‐output equations with time‐delays

“…In this article we look for realizations of nonlinear single‐input single‐output (SISO) retarded control systems in the feedforward form. The importance of the feedforward form comes from its triangular structure, which has been useful in designing stabilizing controllers (see Reference 5 for delay‐free and References 6‐8 for time‐delay case). However, why should one study this problem at all?…”