Memoryless State Feedback Research Articles

Guaranteed cost control of time-delay chaotic systems via memoryless state feedback

Abstract This paper studies the problem of guaranteed cost control for a class of time-delay chaotic systems via memoryless state feedback. A design procedure is proposed to construct a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and achieves an adequate level of performance. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Refined Stability Conditions for Linear Uncertain Systems With Multiple Time-Varying Delays

This paper mainly proposes distinct criteria for the stability analysis and stabilization of linear uncertain systems with time-varying delays. Based on the Lyapunov theorem, a sufficient condition of the unforced systems with single time-varying delay is first derived. By involving a memoryless state feedback controller, the condition will be extended to treat with the resulting closed-loop system. These explicit criteria can be reformulated in LMIs forms, so we will readily verify the stability or design a stabilizing controller by the current LMI solver. Furthermore, the considered systems with multiple time-varying delays are similarly addressed. Numerical examples are given to demonstrate that the proposed approach is effective and valid.

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

ABSTRACTThis paper considers the problems of robust non‐fragile stochastic stabilization and H∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.

Robust Control Design for Retarded Discrete-Time Systems

This paper focuses on the analysis and synthesis of a robust stabilizing controller for linear discrete time systems with norm-bounded time varying uncertainties. Delay independent robust stability conditions are derived and two synthesis methods are presented. One method is to construct a robust memoryless state feedback control law from the solutions of linear matrix inequalities. The other method consists of designing robust observer-based output feedback controller. The results are expressed in termes of linear matrix inequalities. A comparison with μ∕LDI tests is presented. Furthermore, numerical examples are given for illustration.

Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays

In this paper, we consider the problems of robust stability and stabilization via memoryless state feedback for uncertain discrete-time switched systems with mode-dependent time-varying delays. By using a descriptor system method and linear matrix inequality technique, and by introducing a switched Lyapunov functional, we establish some new delay-dependent stability and stabilization criteria for the system. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.

DECENTRALIZED DISTURBANCE ATTENUATION FOR LARGE-SCALE NONLINEAR SYSTEMS WITH DELAYED STATE INTERCONNECTIONS

The problem of decentralized disturbance attenuation is considered for a new class of large-scale nonlinear systems with delayed state interconnections. This class of large-scale time-delay systems broadens most existing classes of large-scale time-delay systems in that the uncertain interconnections are bounded by general nonlinear functions instead of linear or polynomial-type functions. It is shown that by decentralized memoryless state feedback control, the closed-loop system achieves internal global asymptotical stability in the sense of Lyapunov and external stability in the sense of L2 gain. Nonlinear Lyapunov-Krasovskii functionals are constructed that render the linear and polynomial-type growth conditions on the interconnections as special cases.

Convex Optimization Approach to Observer-Based Stabilization of Uncertain Linear Systems

New sufficient linear matrix inequality conditions guaranteeing the stability of uncertain linear systems by means of dynamic output feedbacks are presented. It is shown that the search of an observer-based controller for this class of systems is fundamentally decomposed into two main problems: robust stability with a memoryless state feedback and observer design with measured uncertainties. Under the fulfilment of the developed linear matrix inequalities conditions, we show that the observer-based problem is solvable without any need for some equality constraints or iterative computational algorithms. Examples showing the potential of the results are presented.

Global stabilization of a class of time-delay nonlinear systems

This paper is concerned with the problem of global stabilization by state feedback and output feedback for a class of time-delay nonlinear systems that are dominated by a triangular system satisfying linear growth conditions. By solving the Lyapunov equation and constructing the appropriate Lyapunov-Krasovskii functionals (LKF), the linear and memoryless state feedback controller and output feedback controller making the closed-loop system globally asymptotically stable (GAS) are explicitly constructed respectively. Comparing our design scheme with the backstepping method which has been widely used to deal with strictly feedback nonlinear systems, our design scheme is much simpler and more efficient. An example is given to show that the proposed design procedures are very simple and efficient.

Delay-dependent stabilization of linear systems with time-varying state and input delays

The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: x ˙ ( t ) = Ax ( t ) + A 1 x ( t - h 1 ( t ) ) + B 1 u ( t ) + B 2 u ( t - h 2 ( t ) ) . In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither ( A , B 1 ) nor ( A + A 1 , B 1 ) is stabilizable.

Delay-dependent H-infinity control for linear descriptor systems with delay in state

A delay-dependent H-infinity control for descriptor systems with a state-delay is investigated. The purpose of the problem is to design a linear memoryless state-feedback controller such that the resulting closed-loop system is regular, impulse free and stable with an H-infinity norm bound. Firstly, a delay-dependent bounded real lemma(BRL) of the time-delay descriptor systems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor model transformation of the system and by taking a new Lyapunov-Krasovsii functional. The introduced functional does not require bounding for cross terms, so it has less conservation.Secondly, with the help of the obtained bounded real lemma, a sufficient condition for the existence of a new delay-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrix inequalities and the solvability of the problem can be obtained by using an iterative algorithm involving convex optimization. Finally, numerical examples are given to demonstrate the effectiveness of the new method presented.

A scheduled controller design of congestion control considering network resource constraints

AbstractIn this paper, we consider a dynamical model of computer networks and derive a synthesis method for congestion control. First, we present a model of TCP/AQM (Transmission Control Protocol/Active Queue Management) as a dynamical model of computer networks. The dynamical model of TCP/AQM networks consists of models of TCP window size, queue length, and AQM mechanisms. Second, we propose to describe the dynamical model of TCP/AQM networks as linear systems with self‐scheduling parameters, which also depend on information delay. Here we focus on the constraints on the maximum queue length and TCP window size, which are the network resources in TCP/AQM networks. We derive TCP/AQM networks as the LPV system (linear parameter varying system) with information delay and self‐scheduling parameter. We design a memoryless state feedback controller of the LPV system based on a gain‐scheduling method. Finally, the effectiveness of the proposed method is evaluated by using MATLAB and the well‐known ns‐2 simulator (Network Simulator Version 2). © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(1): 61–68, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10341

Delay-dependent stability and H∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays

This paper considers the problems of stability, stabilization and H ∞ control via memoryless state feedback for uncertain discrete-time Markovian jump linear systems with mode-dependent time delays. Based on linear matrix inequalities, delay-dependent solutions are obtained by using a descriptor model transformation of the system and by applying a new bounding technique for cross terms. Numerical examples are presented to illustrate the usefulness of the theoretical results.

Adaptive Robust Tracking and Model Following of Uncertain Dynamical Systems With Multiple Time Delays

The problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In this note, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances, are unknown. An improved adaptation law with /spl sigma/-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with /spl sigma/-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, a numerical example is given to demonstrate the validity of the results.

Non-fragile positive real control for uncertain linear neutral delay systems

This paper is concerned with the problem of non-fragile positive real control for uncertain neutral delay systems with time-invariant norm-bounded parameter uncertainty. Time delays are assumed to appear in both the state and the controlled output equations. The state feedback gains are with norm-bounded controller uncertainties. For both the cases with additive and multiplicative controller uncertainties, we address the problem of designing memoryless state feedback controllers such that, for all admissible uncertainties, the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of desired controllers are given in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the expected memoryless state feedback controller can be easily constructed via convex optimization. An illustrative example is given to demonstrate the validity and applicability of the proposed approach.

Guaranteed cost control for uncertain markovian jump systems with mode-dependent time-delays

This note concerns the robust guaranteed cost control problem for a class of continuous-time Markovian jump linear system with norm-bounded uncertainties and mode-dependent time-delays. The problem is to design a memoryless state feedback control law such that the closed-loop system is stochastically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on linear matrix inequality, delay-dependent sufficient conditions for the existence of such controller are derived by using a descriptor model transformation of the system and by applying Moon's inequality for bounding cross terms. Sufficient conditions which depend on the difference between the largest and the smallest time-delays are also presented. Two numerical examples are given for illustration of the proposed theoretical results.

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.

Delay-dependent robust H∞ control for uncertain systems with a state-delay

A robust H ∞ control for uncertain linear systems with a state-delay is described. Systems with norm-bounded parameter uncertainties are considered and linear memoryless state feedback controllers are obtained. Firstly, a delay-dependent bounded real lemma for systems with a state-delay is presented in terms of linear matrix inequalities (LMIs). By taking a new Lyapunov–Krasovsii functional, neither model transformation nor bounding for cross terms is required to obtain delay-dependent results. Secondly, based on the bounded real lemma obtained, delay-dependent condition for the existence of robust H ∞ control is presented in terms of nonlinear matrix inequalities. In order to solve these nonlinear matrix inequalities, an iterative algorithm involving convex optimization is proposed. Numerical examples show that the proposed methods are much less conservative than existing results.

Robust H∞ control for uncertain singular systems with state delay

AbstractThis paper addresses the problem of robust H∞ control for uncertain continuous singular systems with state delay. The singular system under consideration involves state time delay and time‐invariant norm‐bounded uncertainty. Based on the linear matrix inequality (LMI) approach, we design a memoryless state feedback controller law, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is not only regular, impulse free and stable, but also meets an H∞‐norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the applicability of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.

Delay-dependent stability analysis of singular linear continuous-time system

The paper deals with the class of singular linear continuous systems. By decomposing the singular linear system with time-delay into slow and fast subsystems, linear matrix inequality (LMI)-based delay-dependent stability and stabilisation conditions are established, and an LMI-based algorithm to design a memoryless state feedback control that stabilises the system is provided. Two numerical examples are solved to show the usefulness and validness of the theoretical results.