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.     

不确定离散系统的输出反馈保性能控制

对一类具有范数有界时变参数不确定性的离散时间系统，研究设计一个输出反馈保性能控制器，使得闭环系统对所有允许的不确定性渐近稳定，且闭环性能指标值不超过某个确定的上界。基于线性矩阵不等式处理方法，证明了保性能控制器的存在性等价于一个线性矩阵不等式的可行性，并用该线性矩阵不等式的可解给出了控制器的构造方法和闭环性能指标的上界。     

A new approach to static output feedback stabilization of linear dynamic systems

The topic of this study is output feedback control of linear control system with output. Use of condensed forms of the linear system under static output feedback (SOF) control is made to derive sufficient conditions for stabilization. A minimal-order control-free observer is presented.     

Robust power control method for wireless sensor networks with static output feedback

This paper proposed distributed strategies for the joint control of power and data rates in a wireless sensor network. By adapting a linear state-space model to describe the network dynamics, the power controller with static output feedback is designed in the case that the transmission signal are not always available and the estimation of the unmeasured states constitutes a crucial task in the network. The existence of the power controller is formulated as the feasibility of the convex optimization problem, which can be solved via a linear matrix inequality (LMI) approach. The proposed algorithm also caters to the uncertainties in the network dynamics. Numerical examples are given to illustrate the effectiveness of the proposed methods.     

Robust control of linear discrete-time systems

Given a linear discrete-time system with additive disturbances, a general methodology for designing a stable control algorithm is shown. The approach is Lyapunov-based with certain liberty of tailoring the candidate function for a given problem. Comparison to the existing solutions based on a variable structure approach is given.     

不确定离散时间系统积分滑模保性能控制

针对不确定离散时间系统,研究其积分滑模（ＩＳＭ）保性能控制的设计问题．将最优保性能积分滑模面设计问题,转化为一个具有线性矩阵不等式（ＬＭＩ）约束的目标函数凸优化问题,给出了最优保性能积分滑模面存在的充分条件,并结合干扰估计器设计相应的保性能控制器．与传统滑模控制相比较,积分滑模保性能控制系统具有全阶滑动模态,系统的鲁棒性得到加强,消除了控制抖振和稳态抖振．仿真结果验证了该方法的有效性．     

Output feedback optimal guaranteed cost control of uncertain piecewise linear systems

This paper proposes the output feedback optimal guaranteed cost controller design method for uncertain piecewise linear systems based on the piecewise quadratic Lyapunov functions technique. By constructing piecewise quadratic Lyapunov functions for the closed‐loop augmented systems, the existence of the guaranteed cost controller for closed‐loop uncertain piecewise linear systems is cast as the feasibility of a set of bilinear matrix inequalities (BMIs). Some of the variables in BMIs are set to be searched by genetic algorithm (GA), then for a given chromosome corresponding to the variables in BMIs, the BMIs turn to be linear matrix inequalities (LMIs), and the corresponding non‐convex optimization problem, which minimizes the upper bound on cost function, reduces to a semidefinite programming (SDP) which is convex and can be solved numerically efficiently with the available software. Thus, the output feedback optimal guaranteed cost controller can be obtained by solving the non‐convex optimization problem using the mixed algorithm that combines GA and SDP. Numerical examples show the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

A note on asymptotic stabilization of linear systems by periodic, piecewise constant, output feedback

This note studies the asymptotic stabilization problem for controllable and observable, single-input single-output, linear, time-invariant, continuous-time systems by means of memoryless output feedback of the form u(t)=k(t)y(t), with k(t) periodic and piecewise constant. A necessary and sufficient condition, together with a simpler to test sufficient condition, given in terms of a bilinear matrix inequality, is presented. A few illustrative examples complete the paper.     

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.     

Output feedback guaranteed cost control of networked linear systems with random packet losses

This article is concerned with the output feedback guaranteed cost control problem for a class of networked control systems (NCSs) with both packet losses and network-induced delays. The packet-loss processes in the forward channel and the backward channel are modelled as two Markov chains. The dynamic output feedback controllers are considered, and the closed-loop NCS is modelled as a discrete-time Markovian system with two modes and unit time delay. By using a properly constructed Lyapunov function and the state transformation technique, a sufficient condition is derived for the closed-loop NCS to be mean-square exponentially stable and ensure a decay rate that can be tuned according to the packet loss situations in the networks. Moreover, design procedures for the guaranteed cost controllers are also presented based on the obtained stability condition and guaranteed cost performance result. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.     

Global stabilization of linear discrete-time systems with bounded feedback

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections (“single hidden layer neural networks”) of simple saturation functions.     

New synthesis algorithm of static output feedback sliding mode control for a class of uncertain systems

Based on a kind of regular form,a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined shding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

基于LMI 的线性时滞系统输出动态反馈镇定

考虑线性时滞系统的输出动态反馈镇定问题.利用自由参数矩阵对闭环系统进行适当变换,并结合相应的Lyapunov-Krasovskii泛函得到了时滞相关的控制器存在性判据.利用控制器参数化方法,将控制器参数与泛函参数的求解归结为线性矩阵不等式解的形式,从而克服了时滞无关性及求解非凸优化问题所导致的保守性.仿真算例验证了结论的有效性.     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈控制律存在的充分条件,证明了优化问题在初始时刻的可行解可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．     

Static output feedback control for stochastic hybrid systems: LMI approach

This paper deals with the stabilization problem of the class of uncertain stochastic hybrid systems. The uncertainties are norm bounded type. Under the complete access to the system mode a static output feedback controller that makes the closed-loop dynamics of this class of systems regular, impulse-free and stochastically stable is designed. The gains of this controller are the solution of some linear matrix inequalities (LMIs).