Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H₂ and H_∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.     

基于PI 控制器的线性系统的鲁棒耗散控制

针对参数具有确定性及不确定性的连续系统,给出两种严格耗散PI控制器的设计方法.首先,系统参数确定时,采用线性矩阵不等式方法,导出了类状态反馈和静态输出反馈严格耗散PI控制器存在的充要条件,并由线性矩阵不等式的可行解构造出严格耗散PI控制器增益的显式表达式;然后,考虑系数矩阵均具有范数有界不确定性时的鲁棒严格耗散控制问题,得到相似的结果;最后,通过数值算例表明了所给方法的有效性.     

Delay-scheduled state-feedback design for time-delay systems with time-varying delays—A LPV approach

This paper is concerned with the synthesis of delay-scheduled state-feedback controllers which stabilize linear systems with time-varying delays. In this framework, it is assumed that the delay is approximately known in real-time and used in the controller in a scheduling fashion. First, a new model transformation turning a time-delay system into an uncertain LPV system is introduced. Using this transformation, a new delay-dependent stability test based on the so-called full block -procedure is developed and from this result, a new delay-dependent stabilization result is derived. Since the resulting LMI conditions depend polynomially on the parameters, a relaxation result is then applied in order to obtain a tractable finite set of finite-dimensional LMIs. The interest of the approach resides in (1) the synthesis of a new type of controller scheduled by the delay value which has a lower memory consumption than controllers with memory (since it is not necessary to store past values of the state), and (2) an easy consideration of uncertainties on the delay knowledge.     

A new LMI condition for robust stability of discrete-time uncertain systems

In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to show that an interesting result appeared recently is a special case of the proposed condition. Numerical examples also demonstrate the merit of the present condition in the aspect of conservativeness over other results in the literature.     

Properties of linear switching time-varying discrete-time systems with applications

We study two discrete-time, linear switching time-varying (LSTV) structures, each of which consists of a periodic switch connected to several linear time-invariant (LTI) systems. Such structures can be used to represent any linear periodically time-varying (LPTV) systems. We give basic properties associated with the LSTV structures in terms of their LTI building blocks, and then apply the results to solve a general approximation problem: How to optimally approximate an LPTV system with period p by an LPTV system with period ? The optimality is measured using norms. The study is extended to general multirate periodic systems.     

时变不确定系统鲁棒控制器设计的新方法

基于包含两个二次项的分段Lyapunov函数,研究了线性时变不确定系统的鲁棒控制器设计问题.所考虑的系统由两个矩阵的凸组合构成,通过引入一个附加矩阵,推导出鲁棒控制器存在的充分条件.该控制器的状态反馈增益的求解问题可以转化为一组带有两个比例参数的线性矩阵不等式的凸优化问题.最后的数值示例说明了该设计方法的可行性.     

Anti-windup design with guaranteed regions of stability for discrete-time linear systems

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.     

Robust fault detection of uncertain linear systems via quasi-LMIs

A novel H_∞ deconvolution filter design method is discussed for fault detection of uncertain polytopic linear systems subject to unknown inputs. The enhancement of fault sensitivity is characterized in terms of an H_- index. By means of the Projection Lemma and Congruence Transformations, a quasi-convex LMI formulation of the design problem is obtained. The effectiveness of the filter is illustrated via a numerical example.     

Stochastic linear quadratic regulation for discrete-time linear systems with input delay

This paper considers the stochastic LQR problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels. The key to our approach is to convert the LQR control problem into an optimization one in a Hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic LQR problem by exploiting the dynamic programming approach. Our solution is given in terms of two generalized Riccati difference equations (RDEs) of the same dimension as that of the plant.     

线性时变系统的一种鲁棒镇定控制器设计方法

针对一类线性时变系统提出一种状态反馈镇定控制器设计方法,该反馈控制器能将线性时变系统转化为一个稳定的定常闭环系统.借助线性系统的特征结构配置参数化方法,得到含待求参数的控制器解析形式,并给出控制器的可解性判据.在满足可解性的基础上,进一步对控制器进行了多目标优化设计,使其在保证系统稳定性的同时,具有良好的鲁棒性和干扰抑制能力.通过一个时变卫星姿态控制系统的实际设计表明了该方法的有效性.     

不确定线性系统迭代学习控制器的设计

推导出采用闭环动态迭代学习律的不确定线性系统收敛充分条件, 把它转化为系统输出反馈H_∞控制问题, 然后用线性矩阵不等式 (LMI)方法系统设计迭代学习控制器, 控制器具有鲁棒性较强、阶次较低等优点. 最后仿真结果表明该设计方法的有效性.     

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput(MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k), k = 0, 1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities■(■), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions,which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part(as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of(A(k + 1), A(k)), k = 1, 2,.... iii) They are distinct from and less restrictive than recent results in the literature.     

On almost invariant subspaces for implicit linear discrete-time systems

The concept of almost invariant subspace for an implicit linear discrete-time system is introduced and studied in detail. It is shown also that for regular homogeneous implicit systems the so-called deflating subspaces can be identified with almost invariant subspaces.     

Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

基于平均驻留时间切换离散线性系统的降阶输出反馈控制

模型降阶作为简化大规模系统的重要工具,一直受到控制界的高度重视.另外,由于在H∞理论指导下所设计的控制器具有维数过高的特点,这将导致控制器的实现和维护受到限制.基于此本文提出了一种平均驻留时间切换离散线性系统降阶输出反馈控制方法.该方法由一个降阶的切换输出反馈控制器和一个对切换控制器在每个切换时刻的状态执行复位规则的监控器组成,该控制器对切换控制器在每个切换时刻的状态进行降阶控制.仿真结果验证了该方法的有效性.     

On designing memory state feedback controller for linear systems with interval time-varying delay

This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays. The time delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds of time-varying delay are available. First, a less conservative delayrange-dependent stability criteria is proposed by using a new interval fraction method. In the process of controller synthesis, the history information of system is considered in the controller design by introducing the lower delay state. Moreover, the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case. Finally, two numerical examples are given to show the effectiveness of the proposed method.     

A repetitive controller for discrete-time passive systems

This work proposes and studies a new repetitive controller for discrete-time systems which are required to track or to attenuate periodic signals. The main characteristic of the proposed controller is its passivity. This fact implies closed-loop stable behavior when it is used with discrete-time passive plants. The work also discusses the energetic structure, the frequency response and the time response of the proposed controller structure. A numerical example is included to illustrate its practical use.