Stability Of Nonlinear Time-delay Systems Research Articles

Exponential stability of nonlinear time-delay systems with delayed impulse effects

The problem of exponential stability for nonlinear time-delay systems with delayed impulses is addressed in this paper. Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for two kinds of delayed impulses (i.e., destabilizing delayed impulses and stabilizing delayed impulses). It is shown that if a nonlinear impulsive time-delay system without impulse input delays is exponentially stable, then under some conditions, its stability is robust with respect to small impulse input delays. Moreover, it is also shown that for a stable nonlinear impulsive time-delay system, if the magnitude of the delayed impulses is sufficiently small, then under some conditions, the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays. The efficiency of the proposed results is illustrated by three numerical examples.

The Effect of Delayed Impulses on Stability of Impulsive Time-Delay Systems

AbstractThis paper investigates the problem of the effect of delayed impulses on stability of impulsive time-delay systems. Two types of delayed impulses are considered, that is, the destabilizing delayed impulses and the stabilizing delayed impulses. Under the assumption of bounded impulse input delays, Lyapunov-type sufficient conditions for stability of nonlinear time-delay systems are derived for each type of delayed impulses. Numerical results are presented to confirm the usefulness of the theoretical findings.

Direct adaptive neural control for stabilization of nonlinear time-delay systems

This paper is concerned with the problem of adaptive neural control for uncertain nonlinear strict-feedback time-delay systems with unknown virtual control coefficients. Radial basis function (RBF) neural networks are employed to directly approximate unknown virtual control signals, and then the adaptive neural control law is constructed by Lyapunov-Krasovskii functionals and backstepping. In order to avoid encountering a large number of adaptive parameters when using RBF neural networks as function approximators, an unknown constant, instead of unknown neural weights themselves, is employed as the estimated parameter. This technique makes only one adaptive parameter tuned online, thus significantly alleviating the burdensome computation. Meanwhile, some continuous functions are introduced to overcome the design difficulty originating from the use of one adaptive parameter. The proposed adaptive control guarantees the boundedness of all the signals in the closed-loop system. Simulation studies are presented to illustrate the effectiveness of the scheme.

Stabilization of nonlinear time-delay systems with input saturation via anti-windup fuzzy design

This investigation considers stability analysis and control design for nonlinear time-delay systems subject to input saturation. An anti-windup fuzzy control approach, based on fuzzy modeling of nonlinear systems, is developed to deal with the problems of stabilization of the closed-loop system and enlargement of the domain of attraction. To facilitate the designing work, the nonlinearity of saturation is first characterized by sector conditions, which provide a basis for analysis and synthesis of the anti-windup fuzzy control scheme. Then, the Lyapunov–Krasovskii delay-independent and delay-dependent functional approaches are applied to establish sufficient conditions that ensure convergence of all admissible initial states within the domain of attraction. These conditions are formulated as a convex optimization problem with constraints provided by a set of linear matrix inequalities. Finally, numeric examples are given to validate the proposed method.

Stabilising predictive control of non-linear time-delay systems using control Lyapunov–Krasovskii functionals

Motivated by using appropriate control Lyapunov function (CLF) as a terminal cost in stabilising receding horizon control of non-linear delay-free systems, the authors propose a predictive control scheme with guaranteed closed-loop stability for non-linear time-delay systems utilising control Lyapunov–Krasovskii functional (CLKF). In this approach, stability can be attained without imposing any terminal constraints. The absence of additional constraints results in a significant speedup in computation. Illustrative example shows the effectiveness of the method.

A Robust Fuzzy Control Approach to Stabilization of Nonlinear Time-delay Systems with Saturating Inputs

This paper deals with the stabilization of uncertain nonlinear time-delay systems subject to input saturation. A nonlinear time-delay system is first represented by Takagi-Sugeno (T-S) fuzzy model, a set of fuzzy implications which are used to characterize local dynamics with actuator saturation. Based on a delay independent stability analysis, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is determined. The fuzzy control law is then developed to maximize the estimation of this domain. The derived conditions are formulated in terms of linear matrix inequalities (LMIs) so that the synthesis of fuzzy controller and the estimation of stability domain can be carried out efficiently. Moreover, a robust stabilization for systems with parameter uncertainties, which are time-varying and norm-bounded, is discussed. Numerical examples of truck-trailer control are provided to demonstrate the effectiveness of the design.

MODEL PREDICTIVE CONTROL FOR NONLINEAR TIME-DELAY SYSTEMS

This paper presents a model predictive controller with guaranteed closed-loop stability for nonlinear time-delay systems. The basic idea of the proposed nonlinear model predictive control (NMPC) scheme is based on previous results in NMPC for systems without delayed states. In particular, an expanded zero terminal state constraint, that takes the delayed states of the system into account, is used in order to guarantee closed-loop stability. The applicability of the proposed NMPC controller is demonstrated considering the control of a continuous stirred tank reactor with recycle stream.

A Lyapunov–Krasovskii methodology for ISS and iISS of time-delay systems

This paper presents a Lyapunov–Krasovskii methodology for studying the input-to-state stability and the integral input-to-state stability of nonlinear time-delay systems. An integral input-state estimate which takes into account non-zero initial conditions is also proposed.

Receding horizon predictive control for nonlinear time-delay systems with and without input constraints

This paper proposes a receding horizon predictive control (RHPC) for nonlinear time-delay systems. The control law is obtained by minimizing finite horizon cost with a terminal weighting functional. An inequality condition on the terminal weighting functional is presented, under which the closed-loop stability of RHPC is guaranteed. It is also shown that the stability can be guaranteed for input-constrained systems under an additional functional inequality constraint on the terminal state trajectory. A special class of nonlinear timedelay systems is introduced and a systematic method to find a terminal weighting functional satisfying the proposed inequality condition is given for these systems. Through a simulation example, it is demonstrated that the proposed RHPC has the guaranteed closed-loop stability for nonlinear time-delay systems with and without input constraints.

Robust stability of nonlinear time-delay systems with applications to neural networks

In the first part of this paper we consider a family of nonlinear time-delay systems with uncertainties. For such systems, we present two types of sufficient conditions for robust stability. One type involves delay independent results while the other type involves delay dependent results. In the second part, we apply these sufficient conditions to a class of time-delay artificial neural networks and obtain practical criteria to test asymptotic stability of the equilibria of these time-delay artificial neural networks, with or without perturbations. These criteria require verification of the definiteness of a certain matrix, or verification of a certain inequality. Our results provide also a method of estimating the domain of attraction of the asymptotically stable equilibria of the time-delay neural networks. The applicability of our results is demonstrated by means of three specific examples.