离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

不确定广义系统的弹性H∞控制

研究了具有范数有界不确定性的广义系统的弹性H_∞控制问题. 首先证明了广义系统的有界实引理可以用一个严格的线性矩阵不等式来描述. 在此基础上, 针对控制器存在加性摄动的情形, 以严格线性矩阵不等式约束条件给出了弹性H_∞状态反馈控制器存在的充分必要条件, 并给出了控制器的显式表示. 算例验证了本文方法的可行性.     

滑模控制一类非线性分布式时滞系统

针对一类状态不可测的非线性不确定分布式时滞系统, 给出了系统滑动模态鲁棒渐近稳定的充分条件. 设计了一类滑模观测器, 同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件. 再应用滑模控制的趋近率方法和基于观测器所得到的估计状态, 综合了一类滑模控制器. 该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.     

Lurie广义系统基于观测器的控制器设计

研究了Lurie广义系统基于状态观测器的控制器设计问题.通过使用Lyapunov稳定性理论,线性矩阵不等式方法,分别给出了状态反馈控制器和观测器的设计方法,并建立了分离原理,进而得到了基于观测器的控制器设计方法.所得结论对广义系统理论本身的发展和实际应用都有非常重要的意义.最后给出了仿真实例.     

LMI-based LSVF control of a class of nonlinear systems with parametric uncertainty: an application to an inverted pendulum system

This work centres around the stabilisation of a nonlinear system containing parametric uncertainty using a new Control Lyapunov Function (using Lie derivatives) which comes up with a linear matrix inequality-based design. The paper has three major contributions. The first one is an extension of a theorem proposed to find the convex-concave bounds of nonlinear function towards robustness. With some restrictions in the structure of the uncertainty, the theory developed here may be applied to find out the bounds of any nonlinear function with uncertainty. The next one is the main contribution of this paper in which the form of the control law obtained is linear and has several advantages from a practical point of view over almost all other nonlinear control techniques. The third one is the expansion of the proposed control scheme towards underactuated systems. To show the effectiveness of the proposed theory the controller design is attempted for both the traditional cart inverted pendulum and the more complex mobile wheeled inverted pendulum model.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

离散T-S模糊广义系统的H∞控制

研究了离散T-S模糊广义系统的H_∞控制问题. 首先引入辅助矩阵变量得到新的容许性条件, 解决了由于矩阵P的不定性, 无法运用Schur补引理处理非线性Lyapunov不等式的问题, 进而得到严格不等式表示的H_∞控制条件.基于模糊Lyapunov函数方法, 分别研究了状态反馈控制器、静态输出反馈控制器、动态输出反馈控制器的构造方法. 所得结论可推广到系统具有范数有界不确定性的情况. 最后通过算例验证方法的有效性.     

Output tracking control for networked control systems with time delay and packet dropout

This article studies the problems of H _∞ output tracking performance analysis and controller design for networked control systems (NCSs) with time delay and packet dropout. By using linear matrix inequality (LMI)-based method, H _∞ output tracking performance analysis and controller design are presented for NCSs with constant sampling period. For NCSs with time-varying sampling period, a multi-objective optimisation methodology in terms of LMIs is used to deal with H _∞ output tracking performance analysis and controller design. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The simulation results illustrate the effectiveness of the proposed H _∞ output tracking controller design.     

Robust stabilization for a class of nonlinear networked control systems

The problem of robust stabilization for a class of uncertain networked control systems （NCSs） with nonlinearities satisfying a given sector condition is investigated in this paper. By introducing a new model of NCSs with parameter uncertainty, network-induced delay, nonlinearity and data packet dropout in the transmission, a strict linear matrix inequality （LMI） criterion is proposed for robust stabilization of the uncertain nonlinear NCSs based on the Lyapunov stability theory. The maximum allowable transfer interval （MATI） can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.     

一类Takagi-Sugeno模糊离散广义系统的稳定性判据

利用Lyapunov方法,研究了一类Takagi-Sugeno(T-S)模糊离散广义系统的稳定性问题．给出了该系统一致正则、因果和稳定的充分条件,并把此条件用线性矩阵不等式(LMI)表示．通过矩阵分解把广义系统的非严格矩阵不等式约束转化成严格的矩阵不等式约束,从而可以用LMI工具箱一次判定系统的稳定性,算例说明所给方法使用方便．