Absolute Stability of Nonlinear Systems with Two Additive Time-varying Delay Components

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.     

Absolute stability of nonlinear systems with two additive time-varying delay components

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.     

控制能量有界的时不变系统线性二次型最优控制*

本文通过新的途径讨论控制能量有界的时不变系统一二次型最优控制问题，文中通过“不亏损的Ｓ－过程”方法将该问题转化成无约束的时不变性二次理优控制问题，从而利用后者的基本结果给出本文问题的最优控制的最优结构造，结果表明此时最优控制仍由一线性状态反馈控制器确定，但其增益矩阵的选择是与初始状态有关的，并且对某些安始状态还可能出现奇异情况。     

一类含多面体不确定性多项式系统鲁棒镇定

针对一类含多面体不确定性的多项式系统,研究其局部稳定鲁棒镇定问题。基于多项式平方和(SOS)技术,将该类非线性控制问题转换为凸的SOS规划问题,并通过引入S-procedure技术,保证了所得结论在局部范围内是有效的。同时,结合参数依赖Lyapunov函数方法,给出了该类系统鲁棒性分析与鲁棒镇定控制问题的充分条件,并将其描述为可由SOS规划技术直接求解的状态依赖线性矩阵不等式约束集。最后,通过数值仿真验证了该方法的有效性。     

奇异Lur'e网络的自适应牵制聚类同步控制

本文分别研究了由奇异和非奇异Lur''e系统组成的具有多种耦合方式时滞复杂动态网络的聚类同步问题. 通过设计一类牵制反馈控制器, 仅控制当前聚类中与其它聚类有直接连接的Lur''e系统, 从而有效减少控制器个数同时降低控制成本. 考虑到网络具有多种耦合方式, 本文合理构造Lyapunov 泛函, 并有效利用扇形条件、非线性函数类概念、S过程以及Lyapunov 稳定性定理等方法, 分别给出奇异和非奇异Lur''e 动态网络实现聚类同步的判定条件. 此外, 为有效节省控制成本, 针对控制强度设计一类自适应更新定律, 从而得到网络实现聚类同步的最优控制强度. 最后, 为了验证所得聚类同步判定条件和控制器的有效性, 对一类典型Lur''e网络聚类同步问题进行了数值仿真.     

Piecewise Lyapunov functions for robust stability of linear time-varying systems

In this paper, we investigate the use of two-term piecewise quadratic Lyapunov functions for robust stability of linear time-varying systems. By using the so-called S-procedure and a special variable reduction method, we provide numerically efficient conditions for the robust asymptotic stability of the linear time-varying systems involving the convex combinations of two matrices. An example is included to demonstrate the usefulness of our results.     

Control of nonlinear systems with compensation of disturbances under measurement noises

ABSTRACT

The control algorithm for nonlinear time-invariant systems with compensation of unknown disturbances under measurement noises is proposed. The dimension of noises is equal to the state vector dimension of the plant. Disturbances can be presented in any equation of the plant model. The novel control law is based on the noise estimator and the disturbance compensator. The accuracy in the steady state depends on the first derivative of disturbance and the smallest component of noise vector. A sufficient condition in terms of linear matrix inequality provides feasibility of the proposed algorithm. The simulations show the efficiency of the proposed method compared with some existing ones.     

Invariant sets techniques for Youla–Kučera parameter synthesis

This article addresses an invariant sets approach for Youla–Ku?era parameter synthesis using linear matrix inequality (LMI) techniques. Given a linear discrete-time observer-based system affected by bounded disturbances and constraints, the proposed technique furnishes the best Youla parameter in terms of finding an invariant ellipsoidal set satisfying the constraints and having the maximal ellipsoidal projection on the state space. Compared with the results obtained for an observer-based design, the synthesis of a Youla parameter provides a larger ellipsoidal projection and an improved sensitivity function. The price to pay for these achievements in terms of robustness is usually a slow closed-loop performance with degraded complementary sensitivity function. In order to obtain a compromise between robustness and performance two methods are proposed: the first method imposes a new bound on the Lyapunov function decreasing speed and the second refers to the pole placement concept. The aforementioned approaches are finally validated in simulation considering position control of an induction motor.     

Stability and stabilisation for time-varying polytopic quadratic systems

This paper develops the problems of local stability and stabilisation for time-varying polytopic quadratic systems. The state-space data is assumed to be dependent on parameters that are measurable in real time and vary in a compact set with bounded variation rates. These problems are solved by utilising the parameter-dependent quadratic Lyapunov function and S-procedure approach. Sufficient conditions for local stability and stabilisation are first formulated as optimisation problems with ‘quasi’ linear matrix inequalities. Simulation examples are then provided to confirm the effectiveness of the given approach.     

On bounded real matrix inequality dilation

We discuss a variation of dilated matrix inequalities for the conventional Bounded Real matrix inequality and other similarly structured inequalities. Here, system matrices are separated from Lyapunov matrix to allow the use of different Lyapunov matrices in multi-objective and robust problems. The search involves a bounded scalar parameter that enters the problem nonlinearly and is dealt with a line search. To demonstrate the benefits of the new dilated matrix inequalities over the conventional ones, an example of controller synthesis with ?₂-gain performance measure (?_∞ control) for a system with polytopic uncertainty (robust problem) has been studied. It is shown that for the resulting robust problem the performance obtained via the dilated form is at least equal to that of the conventional one. Also, the connection between the proposed dilated form and the Full Block S-procedure is discussed.