Control For Uncertain Neutral Systems Research Articles

Finite-Time Sliding Mode Control for Uncertain Neutral Systems With Time Delays

The finite-time stability (FTS) problem of uncertain neutral time-delay systems via a sliding mode control (SMC) approach is discussed in this paper. First, we construct a suitable sliding mode surface and an SMC law, which can guarantee the system states can reach the sliding mode surface in a finite time and maintain the sliding mode. Then, through the Lyapunov stability theory and the inequality techniques, the finite time stability of the closed-loop system during reaching phase and sliding mode phase is studied, a set of sufficient conditions which ensure the system to be finite-time stability is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the results.

Guaranteed Cost Control for Uncertain Neutral Systems with a Minimal Order Observer

This paper presents a design scheme of a minimal order observer-based guaranteed cost controller for uncertain neutral systems, in which some state variables can not be measured. The uncertainties are assumed to be norm-bounded. The initial state is assumed unknown but their mean and covariance are assumed known. A sufficient condition for robust stability analysis and robust stabilization are derived via linear matrix inequalities (LMIs). To show the advantage of the proposed method, a numerical example is given.

Novel compensation-based non-fragile H ∞ control for uncertain neutral systems with time-varying delays

This article studies the non-fragile H ∞ control problem for a class of uncertain linear neutral systems with time-varying delays, where the delay in neutral-type term includes a fast-varying case (i.e. the derivative of delay is more than one), which is seldom considered in current literature. The less conservative delay-dependent H ∞ control results for this systems are proposed by applying a new Lyapunov–Krasovskii functional and a geometric series compensation method. Based on the new functional, the systems with fast-varying neutral-type delay can be handled. The benefit brought by applying the compensation method is that many more useful elements can be included in criteria, which are generally ignored when estimating the upper bound of the derivative of Lyapunov–Krasovskii functional. A numerical example is provided to verify the effectiveness of the proposed criteria.

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

Improved robust ℋ ∞ control for neutral systems via discretised Lyapunov-Krasovskii functional

This paper deals with the robust stability analysis and robust control synthesis with guaranteed performance index for time-invariant uncertain neutral systems based on linear matrix inequalities (LMIs). The novelty is to extend the discretisation technique introduced by K. Gu for an appropriate parameter-dependent Lyapunov–Krasovskii functional. Then, the approach proposed improves the previous criteria from the literature that treats robust stability and control for uncertain neutral systems. The main strategy used to derive the obtained conditions is to introduce slack variables allowing one to decouple the system matrices from the Lyapunov functional matrices, without including additional dynamics. Two numerical examples are performed to support the theoretical predictions. The first example deals with stability analysis and the other illustrates how the proposed approach may provide a better solution for the ℋ ∞ guaranteed cost control problem when compared with others available in the literature.

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.

Nonfragile $H_{\infty}$ Control for Uncertain Neutral Systems With Time-Varying Delays via the LMI Optimization Approach

The nonfragile Hinfinity control problem for a neutral system with time-varying delays is considered. Delay-dependent criteria are proposed to guarantee the stabilization and disturbance attenuation of systems. A linear matrix inequality optimization approach is used to solve the nonfragile Hinfinity control problem. Nonfragile Hinfinity control for an unperturbed neutral system is investigated first. Then, nonfragile Hinfinity control for an uncertain neutral system is derived directly from the unperturbed case. Finally, two examples are illustrated to show the improvement of this correspondence.

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.

Guaranteed cost output control for uncertain neutral systems with time-varying delays via LMI

In this paper, the robust guaranteed cost output control for a class of uncertain neutral system with time-varying delays is considered. Based on Lyapunov–Krasovskii functional theory, some stabilization criteria are derived and guaranteed costs are given. Delay-dependent and delay-independent criteria are proposed for the stabilization of the system. Static output linear feedback control is considered to stabilize the uncertain neutral system. Linear matrix inequality (LMI) approach and parametrizing transformation approach are used to solve the stabilization problems. A procedure for the controller design is provided. Optimal guaranteed cost output control will be achieved when the optimization problem under LMI conditions can be solved. Finally, two numerical examples are illustrated to show the use of the results.

Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

In this paper, delay-dependent guaranteed cost observer-based control for neutral systems with time-varying delays is considered. Control and observer gains will be given from the linear matrix inequality feasible solutions. Optimal guaranteed cost observer-based control which will minimize the guaranteed cost of the system is provided.

Delay-dependent robust H∞ control of uncertain neutral systems with state and input delays: LMI optimization approach

Abstract The H ∞ robust control problem for a class of uncertain neutral system with both state and input delays is considered. By choosing a Lyapunov–Krasovskii functional, some delay-dependent criteria are proposed to guarantee stabilization and disturbance attenuation of the systems. Linear matrix inequality (LMI) optimization approach is used to solve the H ∞ control disturbance attenuation problem. Significant improvement for the delay-dependent results has been reached. Computer software Matlab can be applied to obtain all the proposed results. Finally, some numerical examples are given to illustrate the improvement archived in this paper.

Delay-dependent and delay-independent guaranteed cost control for uncertain neutral systems with time-varying delays via LMI approach

This paper investigates the robust guaranteed cost control for a class of uncertain neutral system with time-varying delays. Based on Lyapunov–Krasovskii functional theory, some stabilization criteria are derived and guaranteed costs are given. Delay-dependent and delay-independent criteria are proposed for the stabilization of our considered systems. State feedback control is considered to stabilize the uncertain neutral system and upper bounds on the closed-loop cost function are given. Linear matrix inequality (LMI) approach and genetic algorithm (GA) are used to solve the stabilization problems. The optimal guaranteed cost control which will minimize the guaranteed cost for the system is provided. A procedure for the controller design is provided. Finally, two numerical examples are illustrated to show the use of our obtained results.

Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input

Abstract This article considers non-fragile guaranteed cost control problem for a class of uncertain neutral system with time-varying delays in both state and control input. Delay-dependent criteria are proposed to guarantee the robust stabilization of systems. Linear matrix inequality (LMI) optimization approach is used to solve the non-fragile guaranteed cost control problem. Non-fragile guaranteed cost control for unperturbed neutral system is considered in the first step. Robust non-fragile guaranteed cost control for uncertain neutral system is designed directly from the unperturbed condition. An efficient approach is proposed to design the non-fragile guaranteed cost control for uncertain neutral systems. LMI toolbox of Matlab is used to implement the proposed results. Finally, a numerical example is illustrated to show the usefulness of the proposed results.

LMI-Based Robust H∞ Control of Uncertain Neutral Systems with State and Input Delays

Robust stabilization and robust H∞ control problems for a class of uncertain neutral system with state and input delays are considered. By choosing a Lyapunov-Krasovskii functional, an alternative delay-dependent sufficient condition for the existence of a controller is derived in terms of linear matrix inequalities. Furthermore, a convex optimization problem can be formulated to obtain an H∞ controller which minimizes an upper H∞ norm bound of the closed-loop state-input delayed system.

Robust control for uncertain neutral systems with time-delays in state and control input via LMI and GAs

In this paper, the problem of robust control for uncertain neutral delay systems in state and control input is considered. The uncertainty under discussed is nonlinear time-varying perturbations and does not require a matching condition but is norm-bounded. Based on the constructive use of Lyapunov functional, delay-dependent stabilization criteria are proposed to guarantee robust stability for the systems via linear control. Linear matrix inequality and genetic algorithms are used to design a memoryless state-feedback controller. An example is given to illustrate our result is less conservative than other.