Memoryless State Feedback Control Law Research Articles

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

SummaryThis paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.

On delay-dependent stabilization of retarded systems-an integral-inequality based approach

In this paper, a new integral-inequality method is proposed by taking both the Leibniz-Newton formula and the discussed system into account. By using a Lyapunov-Krasovskii functional approach combined with the new integral inequality, we present the new stabilization criteria for the time-delay system which employs a memoryless state feedback control law. We exert ourselves to find a less conservative transformation way by bringing the free weighting matrices into the integral inequality, and also these free matrices express greatly the relationships among the system variables and among the terms in the Leibniz-Newton formula. The techniques applied here improve the results in existing literature. The results obtained by solving LMIs in this note are illustrated to be less conservative comparing with the previous ones. Moreover, numerical examples demonstrate the validity and the evident superiority of the proposed criteria. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems

This paper deals with the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Then, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. Numerical example is given to illustrate the effectiveness of the developed techniques.

Adaptive Stabilization Control of a Class of Large-scale Stochastic Nonlinear Systems with Time-delays and Unknown Virtual Control Coefficients

In this paper,the adaptive stabilization problem is investigated for a class of large-scale stochastic time-delay nonlinear systems with unknown virtual control coefficients and unknown noise covariances.First,corresponding to the unknown virtual control coefficients and unknown noise covariances,some parameters to be estimated are properly chosen. Then,in view of the effect of the time-varying delay on the stability of the closed-loop system,an suitable Lyapunov- Krasovskii functional is constructed,based on which and the well-known integrator backstepping method,a memoryless state-feedback control law is systematically designed.Under some mild conditions,it is shown that the equilibrium of the closed-loop system is globally stable in probability,and all the signals of the closed-loop system except for parameter estimates converge to zero almost surely.A simulation example is given to illustrate the effectiveness of the proposed approach.

Delay-dependent robust ℋ ∞ control for uncertain stochastic time-delay system

This article deals with the problem of robust stabilisation and ℋ∞ control for a class of uncertain stochastic time-delay system. The parametric uncertainties are real time-varying and norm bounded. The aim is to design a memoryless state-feedback control law such that the closed-loop system are robustly stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such control law are presented based on the linear matrix inequalities approach. Numerical examples are given to illustrate the effectiveness of the developed techniques.

Delay‐dependant robust stability and stabilization conditions for a class of Lur'e singular time‐delay systems

AbstractThe problem of the delay‐dependant robust stability and stabilization is dealt with for a class of Lur'e singular system with state time‐delays in this paper. The new concept of generalized robust quadratic stability and generalized robust quadratic stabilization is presented. Furthermore, the sufficient condition of the robust stability and stabilization is also proposed based on linear matrix inequalities. The synthesis problem addressed is to design a memoryless state feedback control law such that the resulting closed‐loop system is regular, impulse free and asymptotically stable for all admissible uncertainties. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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 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.

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.

On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays

In this article, the nonfragile guaranteed cost control problem is studied for a class of uncertain dynamic systems with multiple time delays and controller gain variation. The multiple time-varying delays are considered. The uncertainty is nonlinear time-varying and is bounded in magnitude. For all admissible uncertainties, time delays, and controller gain variations, the problem is to design a memoryless state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function. Several criteria for the existence of such controllers are derived using the Lyapunov method. A feature of the proposed method is that an upper bound on the guaranteed cost is minimized by solving a convex optimization problem with linear matrix inequalities. A numerical example is given to illustrate the proposed method.

Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays

The guaranteed cost control problem is studied in this paper for a class of uncertain linear discrete-time systems with both state and input delays and a given quadratic cost function. The uncertainty in the system is assumed to be norm-bounded and time-varying. 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. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach, a parametrized characterization of the guaranteed cost controllers (if they exist) is given in terms of the feasible solutions to a certain LMI. Furthermore, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

H∞ controller and observer design for linear systems with point and distributed time-delays

A memoryless state feedback control law is developed such that the closed-loop system containing point and distributed time-delays is asymptotically stable and the H∞-norm of the transfer function from the disturbance to the controlled output is reduced to some predefined level. The feedback is obtained by solving a parameter-dependent linear matrix inequality. When the state variables are not available, an observer is built using a similar technique which generates an estimation of the state variables in order to implement the above state feedback.

Delay-dependent robust H∞ control for uncertain systems with time-varying delays

The paper deals with the robust H∞ control problem for uncertain linear systems with multiple state delays. The parameter uncertainties are time varying and unknown, but are norm-bounded, and the delays are time varying. Based on the LMI approach, a new method for designing a robust memoryless state feedback control law is proposed to stabilise this class of uncertain time-delay systems, and to reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The results depend on the size and the varying rate of the delays and may be less conservative.

H∞ Control of discrete-time linear systems with norm-bounded uncertainties and time delay in state

This paper deals with H ∞ control problem for discrete-time linear systems with norm-bounded uncertainties and time delay in state. In terms of a modified Riccati inequality for discrete-time linear systems, a sufficient condition is presented and a state feedback control law is also given. The proposed control law is a memoryless state feedback control law.

Robust stabilization of linear continuous systems subjected to time-varying state delay and perturbations

In this paper, we address the robust stabilization problem by a memoryless state feedback of linear continuous systems including state time delay and parametric perturbations. Both time delay and parametric perturbations are time-varying and two classes of highly structured and unstructured perturbations are discussed respectively. By making use of the Lyapunov stability approach associated with norm or matrix measure techniques, a new stabilizability criterion and the corresponding memoryless state feedback control laws that guarantee to stabilize the mentioned system are developed. The main feature of the present schemes is that the proposed stabilizability criterion does not involve any matching conditions. Besides defining a family of allowable memoryless state feedback control laws to stabilize the time-delay systems with any one of the two classes of perturbation, it can also determine feedback controllers to guarantee that the closed-loop system have a specified stability degree. Finally, we give a numerical example and computer simulations to confirm the validity and to demonstrate the applicability of the present schemes.

Robust stabilization for uncertain time-delay systems containing saturating actuators

A class of uncertain time-delay systems containing a saturating actuator is considered. These systems are characterized by delayed state equations (including a saturating actuator) with norm-bounded parameter uncertainty (possibly time varying) in the state and input matrices. The delay is assumed to be constant bounded but unknown. Using a Razumikhin approach for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws. These bounds are given in terms of solutions of appropriate finite dimensional Riccati equations.

Memoryless H∞ controller design for linear systems with delayed state and control

We present a memoryless H∞ control design method for linear time-invariant systems that have no parametric uncertainty but delay in the state and control. Based on the Riccati-equation approach, we design a memoryless linear time-invariant state feedback control law, which guarantees the asymptotic stability of the closed-loop control system and reduces the effect of the disturbance input on the controlled output to a prescribed level.

A feedback control law for nonlinear time lag systems

A simple memoryless state feedback control law is derived for a class of nonlinear time lag systems. Some well known techniques are used to transform a nonlinear time lag system in suitable coordinates in which the design of the control law is straightforward. In certain cases, the asymptotic stability of the closed loop system is ensured independently of delay values.