Design of observers for non-linear time-varying systems

Novel stable observers are proposed for discrete, time-varying systems having time-varying, sector-bounded non-linearities. First, the form of the non-linearity is assumed to be known for all time and a stable non-linear filter is presented. Then assuming that the form of the non-linearity is not known but only a sector bound is given, we propose a linear filter and an upper bound on the sector constant to obtain a stable observer. The convergence conditions for the proposed observers are given directly in terms of the design parameters and are, therefore, very easy to check.     

Design of low-order delayed-measurement observers for discrete-time linear systems

This paper considers the development of a discrete-time low-order delayed-measurement observer for a discrete time-invariant linear system. The observer has several unique features. It uses discrete-time delayed measurements as part of its inputs and it is an rth-order observer for an nth-order linear system with q linearly dependent outputs, where r <n ? q. The purpose of this observer is to implement the control directly without estimating the state first. It is shown that under certain conditions the dimension of the observer is much lower than the standard observer of dimension n?q. The procedure employed here presents an approach which can be very important in large-scale control implementation.     

连续切换非方广义线性系统的观测器设计

针对一类连续切换非方广义线性系统,设计了广义状态观测器,并分析了状态估计误差的稳定性。首先通过矩阵的初等变换将连续切换非方广义线性系统的观测器设计问题转换为连续切换广义线性系统的观测器设计问题,之后设计第i个子系统的子观测器,可根据第i个子观测器构造这个广义切换系统的观测器。当观测器是全维观测器,且每个子系统都可检测时,状态估计误差甚至可以在任意切换下指数收敛到零。最后,通过数值实例和Matlab仿真分析说明了观测器设计方法简单可行,观测误差较其他方法的收敛速度快,证实了该方法的有效性和正确性。     

广义系统区间观测器设计

对于不确定或者未知输入系统, 常规鲁棒观测器设计对系统和干扰有较多限制条件. 区间观测器对系统具有宽松的前提条件, 且对干扰只要求有界, 因而区间观测器更具有广泛性. 针对离散和连续的广义未知输入系统, 研究区间观测器的设计问题, 通过对离散系统和连续系统进行不同的变换, 将系统转化为易于求取区间观测器系数矩阵的形式; 然后基于相同的参数求取方式, 给出广义系统区间观测器的设计方法. 仿真结果表明了所提出方法的有效性和正确性.

     

Design of single-functional observers for linear time-varying multivariable systems

A method is presented for the design of an observer capable of reconstructing a single linear functional of the states of a linear time-varying system. The method is based on a canonical transformation of uniformly observable time-varying multi-variable system. It is shown that this canonical form, along with certain pre-specified structures of observer coefficient matrices, leads to a systematic and straightforward procedure for designing a functional observer of minimal order.     

广义线性系统的干扰解耦观测器设计

提出了广义线性系统的Luenberger函数观测器关于干扰解耦的充要条件,并进一步基于广义Sylvester矩阵方程的显式通解给出了干扰解耦观测器的参数化设计方法.这种方法首先给出了观测器增益矩阵的参数表示,然后通过结合观测器增益矩阵的参数表示和提出的干扰解耦条件,给出了设计广义线性系统干扰解耦观测器的算法.数值例子说明了本文设计方法的有效性.     

Reduced-order observers for linear discrete-time systems

Luenberger's observer is considered as an alternate to the Kalman filter for obtaining state estimates in linear discrete-time stochastic systems. An interesting new solution to the problem of constructing optimal and suboptimal reduced-order observers is presented. The solution contains as special cases both Kalman's optimal filter and the optimal minimal-order observer of Leondes and Novak. Also, the Tse and Athans observer is obtained as a special case of the reduced-order observer solution.     

Luenberger observers for switching discrete-time linear systems

State estimation is considered for a class of switching discrete-time linear systems. The switching is assumed to be unknown among the various system modes associated with different known matrices. The proposed scheme relies on the combination of the estimation of the system mode with the application of a Luenberger-like observer whose gain is a function of the estimated mode. In the absence of noises, the estimate of the mode can be chosen among the ones that are consistent with the measurements and the stability of the estimation error is ensured under suitable conditions on the observer gains. Such conditions can be expressed by means of linear matrix inequalities (LMIs). The presence of bounded disturbances is also taken explicitly into consideration. In this situation, a novel method based on a minimum-distance criterion is proposed in order to estimate the system mode. Also in this case the error of the resulting estimator is proved to be exponentially bounded.     

Stable adaptive observers for nonlinear time-varying systems

An adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described. Sufficient conditions for stability of this observer are provided. These conditions are in terms of the structure of the system and canonical form, the boundedness of the parameter variations, and the sufficient richness of some signals. The scope of the canonical form and the use of the observer/identifier is motivated by the presentation of applications to time-invariant bilinear systems, nonlinear systems in phase-variable form a biotechnological process, and a robot manipulator. In each case, the specific stability conditions are presented     

Sliding mode state observers for discrete-time linear systems

In discrete-time systems, instead of having a hyperplane as in the continuous case, there is a countable set of points comprising a so-called lattice; and the surface on which these sliding points lie is named the latticewise hyperplane. In this paper an asymptotically stable observer for discrete-time systems is designed by using the properties of the sliding mode such that the stability of the error system in the sliding mode is maintained. Various techniques for finding the feedforward injection map are proposed. The stability of the reconstruction error system with a bounded perturbation signal is studied.