Stability analysis and control for switched stochastic delayed systems

This paper investigates almost sure exponential stability and feedback stabilization for switched time‐delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non‐convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean‐square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Controller design and analysis for singularly perturbed switched systems with actuator saturation

This paper investigates the problems of controller design and stability analysis for singularly perturbed switched systems subject to actuator saturation. A set of well‐defined sufficient conditions for the existence of state feedback controllers is proposed, under which the closed‐loop system is locally asymptotically stable for arbitrary switching law as long as the singular perturbation parameter is sufficiently small. With the obtained controller, the estimation problem of stability bound and basin of attraction of the closed‐loop system is reduced to solving a convex optimization problem. A numerical example and a hydraulic servo position system are used to illustrate the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

Optimal Control of Switching Times in Switched Stochastic Systems

In this paper, we solve an optimal control problem for switched stochastic systems using calculus of variations, where the objective is to minimize a cost functional defined on the state and the switching times are the sole control variables. In particular, we focus on the problem in which a pre‐specified sequence of active subsystems is given. For one switching time case, the derivative of the cost functional with respect to the switching time is derived, which has an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instant. Then, we propose an approach to deal with the problem with multi‐switching times case. Finally, two numerical examples are given, highlighting the viability and advantages of the proposed methodology.     

一种减少SRM转矩脉动的控制策略研究

开关磁阻电机(SRM)由于其简单的结构和优异的性能,应用范围很广泛,但其本身结构导致了转矩脉动的产生,为了解决这个问题,文章研究了一种控制策略—直接转矩控制,以减少开关磁阻电机的转矩脉动。文章详细阐述了直接转矩控制的基本原理和实现方法,并对基于这种控制策略的开关磁阻电机的控制进行了Matlab仿真。仿真结果表明直接转矩控制能够有效地减少开关磁阻电机的转矩脉动,且控制方法简单,系统具有良好的动静态性能。     

一种八阶开关电容带通滤波器的设计

采用数模混合CMOS工艺,设计了一种八阶开关电容带通滤波器以及辅助的低通抗混叠滤波器和平滑滤波器。仿真结果表明设计的开关电容滤波器实现了中心频率57KHz,通带增益20dB,3dB带宽3KHz,阻带衰减35dB。设计的开关电容滤波器在一款RDS解调芯片中成功实现了RDS信号的中频选择功能。     

具有圆盘极点约束的不确定切换系统的鲁棒控制

本文研究了一类具有圆盘极点约束的不确定线性切换系统的鲁棒镇定问题．对此类系统设计了状态反馈控制器,使得闭环系统的所有极点均位于一个给定的圆盘中,并得到了一个基于LMI的充分条件．通过求解线性矩阵不等式,可以构造一个具有较小反馈增益参数的状态反馈控制器．最后的仿真算例证明了本文结果的有效性。     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

Output feedback control for uncertain linear systems with faulty actuators based on a switching method

This paper investigates the problem of output feedback stabilization for a class of uncertain linear systems with faulty actuators via the synergy with a switching strategy. When actuators suffer a ‘destabilizing failure’ and the never‐faulty actuators cannot stabilize the given system, the closed‐loop exponential stability can still be achieved via the average dwell‐time scheme employing an arbitrary switching signal. The prerequisite condition found requires the ratio between the two lapse times, when the system is devoid of faulty actuators and when it is not so, to be less than a certain specified constant. Then the stabilizing output feedback controls are designed via the technique of linear matrix inequalities. The illustrative example and the respective simulation results demonstrate the feasibility and effectiveness of the proposed design synthesis. Copyright © 2008 John Wiley & Sons, Ltd.     

A new adaptive backstepping Coulomb friction compensator for servo control systems

A new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time‐derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time‐variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society