Class Of Uncertain Neutral Systems Research Articles

New Criterion of Robust Hܣ Stabilization for Uncertain Neutral Systems

The problems of delay-dependent robust stability and stabilization for a class of uncertain neutral systems are investigated in this paper. At first, by constructing a new Lyapunov functional and using the Lyapunov stability theory, a new delay-dependent condition which renders the system with no external disturbance and input to be asymptotically stable is obtained and given by a linear matrix inequality. Then, based on the obtained condition, a state feedback stabilize law is designed, which guarantees closed-loop neutral systems are asymptotically stable for all the permitted uncertainties when the external disturbance is naught, and it can also guarantee the closed-loop systems have performance under the external disturbance. The model of neutral systems with both the uncertainty and the disturbance discussed in this paper has rarely been considered before.

Improved Results on Delay-Dependent Robust H ∞ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

Adaptive Robust Control for a Class of Uncertain Neutral Systems with Time Delays and Nonlinear Uncertainties

The problems of robust stabilization and adaptive robust controller design are considered for a class of uncertain neutral systems with time delays and nonlinear uncertainties. In this paper, Pade approximation is used to deal with input-delays, and the adaptation laws are proposed to estimate the norm of the unknown parameter uncertainties. Based on the improved Razumikhin-type theorem and the updated values, a class of delay-independent adaptive robust state feedback controllers is constructed to guarantee the uniform ultimate boundedness of uncertain neutral systems with input-delays and nonlinear uncertainties. Finally, the chemical two-stage dissolution tank is used to illustrate the effectiveness of the proposed method.

Tracking control on target signal for a class of uncertain neutral systems

Tracking control based on target signal for a class of uncertain neutral systems is investigated in this paper. An augmented error system is constructed by combining the control system with the target signal. Through a Lyapunov-Krasovskii function and some inequalities, a stability criterion in terms of LMIs is proposed for the auto-controlled system. Then a state feed-back control is designed for the augmented error system. And tracking control, where the target signal and error signal are utilized to help deduce the static error, is obtained for the original uncertain neutral system. A numerical example is given to illustrate the validity of our proposed method.

Robust passive control for a class of uncertain neutral systems based on sliding mode observer

The passivity-based sliding mode control (SMC) problem for a class of uncertain neutral systems with unmeasured states is investigated. Firstly, a particular non-fragile state observer is designed to generate the estimations of the system states, based upon which a novel integral-type sliding surface function is established for the control process. Secondly, a new sufficient condition for robust asymptotic stability and passivity of the resultant sliding mode dynamics (SMDs) is obtained in terms of linear matrix inequalities (LMIs). Thirdly, the finite-time reachability of the predesigned sliding surface is ensured by resorting to a novel adaptive SMC law. Finally, the validity and superiority of the scheme are justified via several examples.

RobustH∞Observer-Based Control of Uncertain Neutral Systems with Mixed Delays

In this paper, the robust In this paper, the robust H ∞ control problem of output dynamic observer-based control for a class of uncertain neutral systems with discrete and distributed time delays is considered. Linear matrix inequality (LMI) optimization approach is used to design the new H ∞ output dynamic controls. The minimal H ∞ -norm bound and the maximal perturbed bound are given. Based on the result of this paper, the constraint of matrix equality is not necessary for designing the H ∞ observer-based controls. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.

Robust Output Observer-Based Control of Neutral Uncertain Systems with Discrete and Distributed Time Delays

In this paper, the robust control problem of output dynamic observer-based control for a class of uncertain neutral systems with discrete and distributed time delays is considered. Linear matrix inequality (LMI) optimization approach is used to design the new output dynamic observer-based controls. Three classes of observer-based controls are proposed and the maximal perturbed bound is given. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.

Observer-Based Robust Passive Control for a Class of Uncertain Neutral Systems: An Integral Sliding Mode Approach

The problem of integral sliding mode control (ISMC) with passivity is investigated for a class of uncertain neutral systems with time-varying delay (NTSTD) and external disturbance. The system states are unavailable. An ISMC strategy is proposed based on the state estimate. By employing a novel sliding functional, a new sufficient criterion of robust asymptotic stability and passivity for both the error system and the sliding mode (SM) dynamic system is derived via linear matrix inequality (LMI) technique. Then, a SM controller is synthesized to guarantee the reachability of the sliding surface predefined in the state estimate space. Finally, a numerical example shows the feasibility and superiority of the obtained result.

An improved delay-dependent criterion for stability of uncertain neutral systems with mixed time delays

This paper addresses the asymptotic stability problem for a class of uncertain neutral systems with discrete and distributed time delays. By considering a new Lyapunov functional involving discrete-delay interval into two equal parts and employing the linear matrix inequality technique together with free weighting matrix approach, less conservative stability criteria are derived to compute the maximum allowable upper bound for the delay-range within which the considered uncertain neutral system is asymptotically stable. The obtained stability conditions are formulated in terms of linear matrix inequalities (LMIs) that can be easily solved by using the MATLABLMI toolbox package. The effectiveness of the proposed stability criterion is demonstrated through a numerical example and the results are compared with some existing works to show the less conservatism of the obtained results.

Robust stability and control for uncertain neutral time delay systems

In this article, the problem of robust stability and stabilisation for a class of uncertain neutral systems with discrete and distributed time delays is considered. By utilising a new Lyapunov functional based on the idea of delay partitioning approach, we employ the linear matrix inequality technique to derive delay-dependent criteria which ensures the robust stability of uncertain neutral systems. The obtained stability conditions are formulated in terms of linear matrix inequalities that can easily be solved by using standard software packages. Further, the result is extended to study the robust stabilisation for uncertain neutral systems with parameter uncertainties. A state feedback controller is proposed to guarantee the robust asymptotic stabilisation for uncertain systems and the controller is constructed in terms of the solution to a set of matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and conservatism of the obtained results. It is shown that the results developed in this article can tolerate larger allowable delay than some existing works in the literature. Further, it is proved that the proposed criterion is also computationally less conservative when compared to some existing results.

Robustness analysis for a class of linear neutral systems in a critical case

This study pays attention to robust stability of a class of uncertain neutral systems in a critical case, where the spectral radius of the principal neutral term (matrix H in this study) is equal to 1. It is shown that usual methods cannot deal with such systems with uncertainties. Thus, a novel method is developed, whose idea is to examine whether or not an existing stability criterion still holds when the uncertainties are sufficiently small. More specifically, it is to examine whether or not the existing stability criterion in terms of a linear matrix inequality (LMI) still has a solution with the sufficiently small uncertainties. By analysing the structure of the solution, a new robust stability criterion is derived in terms of the existence of solutions to an equation. An application shows the effectiveness of the proposed method by dealing with a problem caused by numerical methods when solving LMIs.

Delay-dependent Stability Criteria for a Class of Uncertain Neutral Systems

Delay-dependent Stability Criteria for a Class of Uncertain Neutral Systems

Robust mixed H2/H∞ delayed state feedback control of uncertain neutral systems with time‐varying delays

AbstractThis paper considers the problem of robust mixed H2/H∞ delayed state feedback control for a class of uncertain neutral systems with time‐varying discrete and distributed delays. Based on the Lyapunov–Krasovskii functional theory, new required sufficient conditions are established in terms of delay‐range‐dependent linear matrix inequalities for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H2/H∞ delayed state feedback control is derived based on a convex optimization method such that the resulting closed‐loop system is asymptotically stable and satisfies H2 performance with a guaranteed cost and a prescribed level of H∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Delay-dependent Stability Criteria for a Class of Uncertain Neutral Systems

In this paper, the problem of delay-dependent stability criteria for a class of constant time-delay neutral systems with time-varying structured uncertainties is investigated. New asymptotic stability criteria are derived in the form of linear matrix inequality. Two numerical examples are given to indicate that the results presented in this paper are effective and less conservative than some existing results.

Integral-inequality approach to delay-dependent robust H-infinity control for uncertain neutral systems

This paper focuses on the design problem of a memoryless state feedback robust H-infinity controller for a class of uncertain neutral systems. By using a newly established integral inequality, a new delay-dependent bounded real lemma for such systems is derived without involving a fixed model transformation. Furthermore, new delay-dependent sufficient conditions for the existence of robust H-infinity controllers are presented in terms of nonlinear matrix inequalities. A design procedure involving an iterative algorithm is also proposed to design such controllers. Numerical examples are given to demonstrate the less conservatism of the proposed method.

Robust Mixed H2/H∞ Control of Uncertain Neutral Systems with Time-Varying Delays

This paper considers the problem of robust mixed H2/H∞ delayed state feedback control for a class of uncertain neutral systems with time-varying discrete and distributed delays. Based on the Lyapunov-Krasovskii functional theory, new required sufficient conditions are established in terms of delay-range-dependent linear matrix inequalities (LMIs) for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H2/H∞ delayed control is derived based on a convex optimization method such that the resulting closed-loop system is asymptotically stable and satisfies H2 performance with a guaranteed cost and a prescribed level of H∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach.

New stability analysis for uncertain neutral system with time-varying delay

In this paper, a class of uncertain neutral system with time-varying delay is studied. Based on Lyapunov functional approach and linear matrix inequality technology, the stability criteria are given, Numerical examples show the effectiveness of our theoretical results and the influence of uncertainties to the stability of the neutral system.

Robust H ∞ Output Dynamic Observer-Based Control Design of Uncertain Neutral Systems

In this paper, the robust H∞ control problem of output dynamic observer-based control for a class of uncertain neutral systems is considered. The linear matrix inequality optimization approach is used to design the new H∞ output dynamic controls. Three classes of H∞ observer-based controls are proposed. The minimal H∞-norm bound and the maximal perturbed bound are given. Based on the result of this paper, the constraint of matrix equality is not necessary for designing the H∞ observer-based controls. A numerical example is given to stress the usefulness of the proposed results.

Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties

The problem of robust stability for a class of uncertain neutral system with time-varying delay and nonlinear uncertainties is studied in this paper. A new delay-dependent stability criteria is presented by using Lyapunov method. The criteria is given in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the developed techniques.

On delay‐dependent LMI‐based guaranteed cost control of uncertain neutral systems with discrete and distributed time‐varying delays

AbstractIn this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov–Krasovskii functional theory, a delay‐dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed‐loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd.