Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method. Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Young Il Lee. Jong-Hae Kim received the B.S., M.S., and Ph.D. degrees in Electronics from Kyungpook National University in 1993, 1995, and 1998, respectively. He was with STRC at Kyungpook National University from Nov. 1998 to Feb. 2002. He has been with Sun Moon University since March, 2002. His research interests focus on robust control, signal processing, and industrial application systems.     

同时含有状态和输入时滞系统的滑模控制

研究同时舍状态和输入时滞的系统交结构控制问题，基于LMI，给出了存在滑动模态的时滞相关的充分条件，利用LMI的解，得到了两种不同的滑动模态和控制器的设计方法，所提出的方法简单量行，具有较小的保守性，可进一步推广到多时滞和不确定时滞系统。     

A closed-form optimal control for linear systems with equal state and input delays

This paper presents the optimal regulator for a linear system with equal delays in state and input and a quadratic criterion. The optimal regulator equations are obtained using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulators available for the linear system without delays and for a rational approximation of the original time delay system. Simulation graphs demonstrating better performance of the obtained optimal regulator are included.     

Reliable guaranteed cost control for linear state delayed systems with adaptive memory state feedback controllers

This paper deals with the problem of reliable guaranteed cost control for linear time‐delay systems via state feedback against actuator faults. Based on indirect adaptive method, the proposed delay‐dependent memory controller with variable gains is established, whose gains are affinely dependent on the online estimations of fault parameters. In the frameworks of linear matrix inequalities, sufficient conditions with less conservativeness than those of the traditional controller with fixed gains are derived such that the closed‐loop system is asymptotically stable and the cost function value is minimized in both normal and faulty cases. Numerical examples are given to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A note on guaranteed cost control for nonlinear stochastic systems with input saturation and mixed time‐delays

ThisIn the system under investigation, the control input is subject to the saturation constraint, and both discrete and distributed time‐delays are taken into consideration. The objective of the addressed problem is to design a state feedback controller such that the resulting closed‐loop system is asymptotically stable in probability and an upper bound is guaranteed on a prespecified quadratic cost function. Sufficient conditions are established for the existence of the desired guaranteed cost control strategy in terms of the solvability of certain Hamilton–Jacobi inequalities. Simulation results demonstrate the correctness and applicability of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

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

The paper proposes a guaranteed cost feedback control for discrete-time uncertain systems with both state and input delays. The delays are assumed to be time-varying and bounded. In addition to norm-bounded parametric uncertainties, the class of admissible uncertainties and nonlinearities of the system comprehend several types of uncertainties frequently investigated in the literature. Using some recent developments, new sufficient conditions for the existence of the guaranteed cost control are given by bilinear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed method.     

Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays

This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.     

An LMI approach to guaranteed cost control for uncertain linear neutral delay systems

This paper considers the problem of guaranteed cost control for uncertain neutral delay systems with a quadratic cost function. The system under consideration is subject to norm‐bounded time‐varying parametric uncertainty appearing in all the matrices of the state‐space model. The problem we address is the design of a state feedback controller such that the closed‐loop system is not only stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is given in terms of a linear matrix inequality (LMI). When this condition is feasible, the desired state feedback controller gain matrices can be obtained via convex optimization. An illustrative example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Non-fragile guaranteed cost control for discrete-time uncertain linear systems

This paper studies the problem of non-fragile guaranteed cost control (GCC) state-feedback design for discrete-time uncertain linear systems. The systems are assumed to have norm-bounded system uncertainties in both the state and the input matrices. The state-feedback gains are assumed to have norm-bounded controller uncertainties which can be either additive or multiplicative. The non-fragile GCC state-feedback designs, which are related to solutions of some matrix inequalities, guarantee the cost of the system to be within a certain bound for all these admissible uncertainties. Our proposed design approach of separating the controller uncertainty from the system uncertainty gives a less conservative solution. A numerical example is given to illustrate the design methods and the design benefits.     

Suboptimal control of linear systems with delays in state and input by orthonormal basis

This paper presents a method for finding the optimal control of linear systems with delays in state and input and the quadratic cost functional using an orthonormal basis for square integrable functions. The state and control variables and their delays are expanded in an orthonormal basis with unknown coefficients. Using operational matrices of integration, delay and product, the relation between coefficients of variables is provided. Then, necessary condition of optimality is driven as a linear system of algebraic equations in terms of the unknown coefficients of state and control variables. As an application of this method, the linear Legendre multiwavelets as an orthonormal basis for L ²[0, 1] are used. Two time-delayed optimal control problems are approximated to establish the usefulness of the method.     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

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: . 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,B₁) nor (A+A₁,B₁) is stabilizable.     

Minimum-energy control for time-varying systems with multiple state and input delays

This paper considers the minimum-energy control problem for a class of time-varying systems with multiple state and input delays. First, a state transform matrix is presented. By using the transform matrix, a system with multiple state and input delays is converted to a formal equivalent one without delay. Then, the optimal problem of the novel system is solved by using the maximum principle. Analytical expressions of the optimal control law and optimal performance are given by two formulas with respect to the state transform matrix. At last, an algorithm is given to solve the analytical expression of the state transform matrix. Simulation results show that the design algorithm is efficient and easy to implement.     

Mixed filtering for uncertain linear systems: A linear matrix inequality approach

The problem of full-order mixed L₂     

Optimal control for linear systems with multiple time delays in control input

This note presents the optimal linear-quadratic (LQ) regulator for a linear system with multiple time delays in the control input. Optimality of the solution is proved in two steps. First, a necessary optimality condition is derived from the maximum principle. Then, the sufficiency of this condition is established by verifying that it satisfies the Hamilton-Jacobi-Bellman equation. Using an illustrative example, the performance of the obtained optimal regulator is compared against the performance of the optimal LQ regulator for linear systems without delays and some other feasible feedback regulators that are linear in the state variables. Finally, the note establishes a duality between the solutions of the optimal filtering problem for linear systems with multiple time delays in the observations and the optimal LQ control problem for linear systems with multiple time delays in the control input.     

含状态和输入时滞的网络控制系统镇定

研究含有更广泛被控对象的网络控制系统镇定问题．假定被控对象含有时变状态和输入时滞,采用Lyapunov-Krasovskii泛函方法分析了系统的稳定性．所提出的方法可转化为线性矩阵不等式的形式,因而可较为容易地求得控制器和广义最大允许时延．仿真结果说明了所提出方法的有效性．     

Resilient guaranteed cost control for uncertain discrete linear jump systems

Robust stochastic stabilization and guaranteed cost control for a class of uncertain discrete-time linear system with Markovian jumping parameters are discussed. Two classes of controller gain perturbations, additive and multiplicative, are considered. The necessary and sufficient conditions for the above problems are derived, which are in terms of positive-definite solutions of a set of coupled linear matrix inequalities (LMIs). Furthermore, resilient guaranteed cost controllers are designed. Finally, numerical examples are presented to illustrate the solvability and effectiveness of the results.     

Guaranteed cost control of linear systems with distributed delays: A complete type functionals approach

The design of a control law guaranteeing an upper bound on the performance index of linear systems with point wise and distributed delay is addressed. The control law is computed through an iterative procedure: at each step, it is the solution that minimizes the Bellman type equation obtained from plugging in the functional of complete type associated to the closed loop system of the previous step. It is shown that at each step, the closed loop system remains into the class of systems with distributed delays, the stability of the closed loop is maintained, and the guaranteed cost does not increase. The allowed continuous time varying norm bounded uncertainties guaranteeing the cost are also characterized. An illustrative example validates the approach.     

Optimal guaranteed cost control of discrete-time uncertain linear systems

This paper considers the problem of constructing a controller which quadratically stabilizes an uncertain system and minimizes a guaranteed cost bound on a quadratic cost function. The solution is obtained via a parameter-dependent linear matrix inequality problem. © 1998 John Wiley & Sons, Ltd.