Interconnected Time-delay Systems Research Articles

New delay-dependent stability analysis for fuzzy time-delay interconnected systems

This paper investigates the delay-dependent stability of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of interconnected continuous-time Takagi–Sugeno fuzzy subsystems. A stability criterion based on fuzzy Lyapunov–Krasovskii functional is proposed to guarantee the asymptotic stability of fuzzy time-delay interconnected systems. In the derivation process, some free fuzzy weighting matrices are introduced among the terms of the system equation to yield less conservative results. The proposed stability criterion can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Finally, two numerical examples are provided to demonstrate the effectiveness of the present method.

Decentralised delay-dependent static output feedback variable structure control

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.

Decentralised Output Feedback Variable Structure Control for Large Scale Time Delay Systems

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. A decentralised delay dependent static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using a Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.

Decentralized Mixed Delay-Dependent/Delay-Independent Stabilization of Interconnected Time-Delay Systems

The problem of decentralized stabilization of interconnected systems that are delay-dependent for some delays and delay-independent for the remaining ones is addressed in this paper. For the purpose, some of the subsystems are grouped to form new larger subsystems. Such a grouping allows all the interconnection delays present among the smaller subsystems to be divided into two groups in the new subsystem description — (i) intraconnection delays, within the larger subsystem, and (ii) interconnection delays, among the larger subsystems. This facilitates delay-dependent stabilization for the intraconnection delays and delay-dependent stabilization for the interconnection delays. An LMI based stabilization criterion is derived for such mixed delay-dependent/delay-independent stabilization of the overall system. A numerical example is presented demonstrating the effectiveness of the developed criterion.

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.

Adaptive Decentralized NN Control of Nonlinear Interconnected Time‐Delay Systems with Input Saturation

AbstractIn this paper, a novel decentralized adaptive neural control scheme is proposed for a class of interconnected large‐scale uncertain nonlinear time‐delay systems with input saturation. Radial basis function (RBF) neural networks (NNs) are used to tackle unknown nonlinear functions. Then, the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique, along with the minimal‐learning‐parameters (MLP) algorithm. The stability analysis subject to the effect of input saturation constraints are conducted with the help of an auxiliary design system based on the Lyapunov–Krasovskii method. The proposed controller guarantees uniform ultimate boundedness (UUB) of all of the signals in the closed‐loop large‐scale system, while the tracking errors converge to a small neighborhood around the origin. An advantage of the proposed control scheme lies in the number of adaptive parameters of the whole system being reduced to one and in the solution of the three problems of “computational explosion,” “dimension curse,” and “controller singularity”. Finally, simulation results along with comparisons are presented to demonstrate the advantages, effectiveness, and performance of the proposed scheme.

A generalized approach to stabilization of linear interconnected time-delay systems

The objective of this paper is to propose a generalized approach to stabilization of systems which are composed of linear time-delay subsystems coupled by linear time-varying interconnections. The proposed algorithms, which are formulated within the convex optimization framework, provide decentralized solutions to the problem of delay-dependent asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness and disturbance attenuation. Then a decentralized structure of dissipative state-feedback controllers is designed to render the closed-loop interconnected system delay-dependent asymptotically stable with strict dissipativity. Numerical examples are presented to illustrate the applicability of the design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Decentralised adaptive robust control of uncertain large-scale non-linear dynamical systems with time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale interconnected non-linear systems with time-varying delays. It is assumed that the upper bounds of the uncertainties and interconnection terms are unknown, and that the time-varying delays are any non-negative continuous and bounded functions, and do not require their derivatives to be less than one. In particular, it is only required that the non-linear interconnection terms, which can also include time-varying delays, are bounded in any non-negative non-linear functions, which are not required to be known for the system designer. For such a class of uncertain large-scale time-delay interconnected non-linear systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed as uniformly exponentially convergent towards a ball that can be as small as desired. Finally, a numerical example is given to demonstrate the validity of the results.

A critical review of nonlinear fuzzy multiple time-delay interconnected systems using the Lyapunov criterion

This paper reviews the development of fuzzy systems and the problem of time delay control in nonlinear systems. Based on this review, a fuzzy Lyapunov method defined in fuzzy blending quadratic Lyapunov functions is proposed from which to derive stability conditions. In the controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller (FLC) by blending all linear local state feedback controllers. Furthermore, the multiple time-delay interconnected systems are considered in the nonlinear fuzzy systems. Key words: Interconnected systems, fuzzy Lyapunov method, linear matrix inequality.

Stability analysis of interconnected time-delay systems in a generalised framework

Stability analysis of interconnected systems with finite as well as arbitrary interconnection delays is considered in this study. For the purpose, subsystems interconnected with finite delays are grouped to form larger subsystems with intraconnection delays. However, these larger subsystems are interconnected with arbitrary delays among themselves. By considering a suitable Lyapunov–Krasovskii functional, a stability criterion is derived in the linear matrix inequality (LMI) framework to study simultaneous delay-independent (for the interconnection delays) and delay-dependent (for the intraconnection delays) stability of the reformed interconnected system. This proposed criterion is useful when one attempts to estimate the tolerable bounds of the intraconnection delays. Finally, a numerical example is considered to illustrate the effectiveness of the proposed criterion.

Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state-measurement and the second utilizes static output-feedback. The decentralized feedback gains in both schemes are determined by convex optimization over linear matrix inequalities. We characterize decentralized linear matrix inequality-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with an γ-level ℒ2-gain. The developed results are tested on a representative example.

Adaptive sliding mode controller design for decentralised model following of large-scale systems with time-varying delay interconnections

The problem of decentralised robust model following is considered for a class of uncertain large-scale systems with time-varying delay interconnections. It is assumed that the upper bounds of uncertainties and interconnections are unknown. For such a class of uncertain large-scale interconnected time-delay systems, some adaptation laws are introduced to updating the unknown upper bounds, and a class of decentralised local adaptive robust sliding mode controllers is proposed by combining a sliding mode controller with the adaptation law. The proposed decentralised local adaptive robust controller can guarantee that the local tracking error of each subsystem decreases asymptotically to zero in the presence of uncertainties and interconnection terms with time-varying delays. Finally, a numerical example is given to demonstrate the validity of the results.

Pinning a Complex Delayed Dynamical Network to a Homogenous Trajectory

Time delay exists in many fields, such as biology, neural network, mechanics, ecology, and so on. It is important for us to investigate the control of interconnected time-delay systems. In this brief, we propose two schemes to pin a complex delayed dynamical network to a homogenous trajectory. In particular, we prove that the delayed dynamical network is asymptotically synchronized with linear feedback control, and it is exponentially asymptotically synchronized with adaptive feedback controllers. We also find that the number of pinned nodes satisfies an inequality for synchronization. Additionally, the coupling matrix is not necessarily symmetric, and the pinned nodes can randomly be selected. Moreover, the linear feedback gain need not be large. Finally, two well-known network models are provided as illustrative examples to confirm the effectiveness of the technique.

Exponential stabilization controller design for interconnected time delay systems

Decentralized robust control problem is investigated for a class of large scale systems with time varying delays. The considered systems have mismatches in time delay functions. A state coordinate transformation is first employed to change the original system into a cascade system. Then the virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem. By choosing new Lyapunov Krasovskii functional, we show that the designed decentralized continuous adaptive controller makes the solutions of the closed-loop system exponentially convergent to a ball, which can be rendered arbitrary small by adjusting design parameters. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed design techniques.

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.

Decentralized robust model reference adaptive control for interconnected time-delay systems

In this paper, the problem of decentralized robust model reference control for a class of interconnected time-delay systems is investigated. The interconnections with time-varying time delays considered are high order and the gains are not known. A class of decentralized adaptive feedback controllers are proposed, which can render the resulting closed-loop error system uniformly ultimately bounded stable. A numerical example is given to show the feasibility and effectiveness of the proposed design techniques.

Adaptive fuzzy control for uncertain interconnected time-delay systems

In this paper, the problem of control for a class of uncertain interconnected time-delay systems is studied. The interconnections of the system possess time-varying delay characteristics, and the bounds of uncertainties are not precisely known. A decentralized adaptive feedback controller is designed, which is independent of the delays. Lyapunov–Krasovskii approach is employed to show that the corresponding closed-loop system is asymptotically stable. A simulation example is given to demonstrate the potential of the proposed techniques.

Nonlinear decentralized state feedback controller for uncertain fuzzy time-delay interconnected systems

In this paper, the perturbed continuous-time interconnected system with time-delay is represented by an equivalent Takagi-Sugeno type fuzzy model having r i rules for each subsystem. Based on Lyapunov stability theorem and Razumikhin theorem, the nonlinear decentralized state feedback fuzzy controllers are proposed to stabilize the whole perturbed fuzzy time-delay interconnected system asymptotically. Under using this nonlinear controller, the design methods only consider the r i fuzzy rules rather than r i × r i rules for each subsystem, that is, we can remove the negative effect of the coupled terms. Therefore, these approaches can be less conservative. Moreover, if all the time-delays of each subsystem are the same for all rules, we shall propose less conservative criteria. These criteria do not need the solution of a Lyapunov equation or a Riccati equation. We also do not need to find a common positive matrix P to satisfy any inequality. The so-called “matching condition” for the interconnection matrices and perturbations are not needed. Finally, a numerical example is given to illustrate the control design and its effectiveness.

Observer-based adaptive control for uncertain time-delay systems

In this paper, we will focus on investigating the observer-based controlling problem of time-delay systems. First, we investigate a class of simple time-delay systems. The corresponding adaptive observer and controller are designed, which are both independent of the time-delays. Based on Lyapunov stability theory, we prove that the closed-loop system is asymptotically stable. Next we further consider the interconnected time-delay system case. The corresponding adaptive observer and controller are designed, we prove that the resulting closed-loop system is also asymptotically stable. Simulations on controlling time-delay systems and interconnected systems are investigated, and the results show that the designed controllers are feasible and efficient.

Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.