离散线性系统高阶积分观测器设计

针对离散线性系统提出一类高阶积分观测器。并且显示这类观测器满足极点配置分离原理，同时给出了这类观测器的存在条件．基于Sylvester矩阵方程的显式参数化通解提出了这类观测器的参数化设计方法．该方法不仅给出了观测器增益矩阵的参数表达式，而且还提供了观测器系统矩阵左特征向量的参数表达式．该设计方法给出了所有的设计自由度，为实现系统的其他性能提供了方便且强有力的工具．数值例子说明了设计过程，并表明了该方法的有效性．     

Robust fault detection in linear systems based on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers （FSO）. Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.     

Robust fault detection in linear systems based on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers (FSO). Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.     

线性系统对偶Luenberger观测器设计

提出了线性系统对偶Luenberger观测器的参数化设计方法.基于一类广义Sylvester矩阵方程的显式参数化解,根据一些自由参数给出了对偶Luenberger观测器所有增益矩阵的参数化表达.该设计方法能提供所有的设计自由度,它们能进一步用来实现系统的其他性能指标.数值例子显示了该方法的设计过程.     

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.     

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.     

Robust fault detection in linear systems based on PI observers

A parametric approach for robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order proportional-integral (PI) observers. The approach is based on a result for PI observer design recently proposed. In terms of the design degrees of freedom provided by the parametric PI observer design and a group of introduced parameter vectors, a sufficient and necessary condition for PI observer design with disturbance decoupling is established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance to the residual signal is decoupled, and a simple algorithm is presented. The presented approach offers all the degrees of design freedom. A numerical example illustrates the effect of the proposed approach.     

一类时滞系统的函数观测器设计

针对一类状态变量中含有时滞的线性系统,提出了函数观测器设计的一种参数方法。给出了函数观测器存在的充要条件。基于Lyapunov稳定理论和广义Sylvester矩阵方程的完全参数化解,给出了时滞系统函数观测器设计算法。两个数值例子说明了提出算法的简单性、有效性。该方法提供了进一步满足其他性能要求的设计自由度。     

Disturbance Decoupled Observers for Systems With Unknown Inputs

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method.      

Eigenstructure assignment design for proportional-integral observers: the discrete-time case

A complete parametric design approach for proportional-integral observers of multivariable discrete-time linear systems is proposed based on an eigenstructure assignment technique. Complete parameterizations for all the observer gains as well as the eigenvector matrix of the observer system matrix are established in terms of three sets of design parameters that satisfy three basic and simple constraints. The proposed approach provides all the degrees of freedom and has great potential in applications. An illustrative example shows the effect of the proposed approach.     

二阶动力学系统高阶PI观测器的参数化设计方法

本文研究二阶动力学系统的高阶比例积分(PI)观测器设计问题．基于Sylvester矩阵方程的解，提出了该观测器设计的参数化方法．该参数化方法给出了该类观测器增益矩阵的参数化表达式，其所含参数除了满足两个约束条件之外是完全自由的．这些参数为控制系统设计提供了全部自由度，可通过优化等手段选择这些参数来满足某些性能要求，如干扰解耦、故障检测和鲁棒性等．此外，该PI观测器的参数化设计方法直接利用二阶动力学系统的原始参数矩阵，只涉及二阶动力学系统n维参数矩阵的运算．给出一个数值例子，以说明所提方法的简单性和有效性．     

Observer parameterization for simultaneous observation

The stable inverse approach is used to obtain the observers for the simultaneous observation of a given set of plants. A parameterization in terms of a stable inverse and a stable null space is proposed for all simultaneous observers. To verify the effectiveness of the proposed method, a design example is also given     

Dissipative interval observer design for discrete‐time nonlinear systems

This paper studies the problem of designing interval observers for a family of discrete‐time nonlinear systems subject to parametric uncertainties and external disturbances. The design approach states that the interval observers are constituted by a couple of preserving order observers, one providing an upper estimation of the state while the other provides a lower one. The design aim is to apply the cooperative and dissipative properties to the discrete‐time estimation error dynamics in order to guarantee that the upper and lower estimations are always above and below the true state trajectory for all times, while both estimations asymptotically converge towards a neighborhood of the true state values. The approach represents an extension to the original method proposed by the authors, which focuses on the continuous‐time nonlinear systems. In some situations, the design conditions can be formulated as bilinear matrix inequalities (BMIs) and/or linear matrix inequalities (LMIs). Two simulation examples are provided to show the effectiveness of the design approach.     

Parametric compensator design in the frequency domain

The parametric approach to the design of observer based compensators has hitherto only been formulated in the time domain. It yields an explicit parametric expression for the state feedback matrix (observer gain) given the closed loop eigenvalues and the corresponding sets of invariant parameter vectors. Using the polynomial approach to the design of observer based compensators this contribution presents an equivalent parameterization in the frequency domain. By introducing the closed loop poles and the set of so-called pole directions as new design parameters, one obtains expressions in parametric form for the polynomial matrix D(s) (D(s)), parameterizing the state feedback (state observer) in the frequency domain. It is shown how the pole directions are related to the invariant parameter vectors used in the time domain approach. Another new result is the parametric design of reduced order observers both in the frequency domain, and derived from those results, in the time domain. The proposed design procedure is also used to provide a parametric solution for the optimal LQG control problem in the presence of partially perfect measurements. Simple examples demonstrate the design procedure.