线性系统的输出反馈特征结构配置——具有不可控不可观模态的情形

本文考虑具有不可控不可观模态的线性系统的输出反馈特征结构配置问题。根据文中给出的矩阵方程AV＋BW＝VF的一种显式参数解，得到了线性系统的输出反馈特征结构配置的一种参数化方法，本文没有对系统附加能控能观条件，在[AB]能控的条件下，本文得到的矩阵方程的解是文[5]中定理2的结果，在[AB]能控且[AC]能观的条件下，本文得到的输出反馈特征结构配置方法是文[6]在系统为定常时算法Ⅱ的结果。     

Analysis of strong and strong periodic detectability of bounded labeled Petri nets

Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and the subsequent states. Different notions of detectability have been proposed in the literature. In this paper, we formalize and analyze strong detectability and strong periodic detectability for systems that are modeled as labeled Petri nets with partial observation on their transitions. We provide three new approaches for the verification of such detectability properties using three different structures. The computational complexity of the proposed approaches is analyzed and the three methods are compared. The main feature of all the three approaches is that they do not require the calculation of the entire reachability space or the construction of an observer. As a result, they have lower computational complexity than other methods in the literature.     

Stability of Riccati's Equation with Random Stationary Coefficients

The purpose of this paper is to study under weak conditions of stabilizability and detectability, the asymptotic behavior of the matrix Riccati equation which arises in stochastic control and filtering with random stationary coefficients. We prove the existence of a stationary solution of this Riccati equation. This solution is attracting, in the sense that if P _t is another solution, then onverges to 0 exponentially fast as t tends to +∞ , at a rate given by the smallest positive Lyapunov exponent of the associated Hamiltonian matrices. Accepted 13 January 1998     

Stochastic Detectability and Mean Bounded Error Covariance of the Recursive Kalman Filter with Markov Jump Parameters

In this article, we study the error covariance of the recursive Kalman filter when the parameters of the filter are driven by a Markov chain taking values in a countably infinite set. We do not assume ergodicity nor require the existence of limiting probabilities for the Markov chain. The error covariance matrix of the filter depends on the Markov state realizations, and hence forms a stochastic process. We show in a rather direct and comprehensive manner that this error covariance process is mean bounded under the standard stochastic detectability concept. Illustrative examples are included.     

Determination of phenols by HPLC down to PPT levels

Summary A mixture of eleven priority pollutant phenols (PPP) have been separated using a Dionex 4000 chromatograph; VAL-U-PAK ODS (250 × 4.6 mm I.D.) column; eluents A: CH₃CN/0.2M NaH₂PO₄/CH₃COOH 40/60/1 and B: CH₃CN with/without gradient; detectors: UV-254 nm and Pulse Amperometric Detector (PAD) with glassycarbon electrode (+1.20V). With preconcentration unit (guard RP-18 column) on line and PAD, detectability limit at ten ppt was achieved. The method has been applied for determination of PPP in tap-water and in leachates from sanitary and industrial landfill sites.     

Robust state estimation and fault diagnosis for uncertain hybrid systems

Robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems. In this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults. Model uncertainties, disturbances and faults are represented as structured unknown inputs. The robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling. Furthermore, the detectability and mode identifiability conditions are rigorously analyzed. On the basis of the robust hybrid observer, a robust fault detection and isolation scheme is presented also in the paper. Simulations of a hybrid four-tank system show the proposed approach is effective.     

New results on general observers for discrete-time nonlinear systems

In this paper, we establish that detectability is a necessary condition for the existence of general observers (asymptotic or exponential) for discrete-time nonlinear systems. Using this necessary condition, we show that there does not exist any general observer (asymptotic or exponential) for discrete-time nonlinear systems with real parametric uncertainty, if the state equilibrium does not change with the parameter values and if the plant output function is purely a function of the state. Next, using center manifold theory for maps, we derive necessary and sufficient conditions for the existence of general exponential observers for Lyapunov stable discrete-time nonlinear systems. As an application of this result, we show that for the existence of general exponential observers for Lyapunov stable discrete-time nonlinear systems, the dimension of the state of the general exponential observer should not be less than the number of critical eigenvalues of the linearization matrix of the state dynamics of the plant.     

On unified concepts of detectability and observability for continuous-time stochastic systems

This paper is concerned with detectability and observability of continuous-time stochastic linear systems. By adopting the idea used in defining these two concepts for time-varying systems and Markovian jump linear systems that have been studied in the literature, corresponding definitions for continuous-time stochastic linear systems are proposed. These two definitions are not only able to unify some recent definitions on these two concept reported in the literature, but also allow us to propose an efficient rank criterion to test observability of continuous-time stochastic linear systems. It seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems. With the help of these two concepts and the new criteria, the stochastic Lyapunov equation is revisited and some recent published work on this equation are generalized. Numerical examples are given to illustrate the effectiveness of the proposed approach.     

New results on general observers for nonlinear systems

In this paper, we establish that detectability is a necessary condition for the existence ofgeneral observers (asymptotic or exponential) for nonlinear systems. Using this necessary condition, we show that there does not exist any general observer (asymptotic or exponential), for nonlinear systems with real parametric uncertainty, if the state equilibrium does not change with the parameter values and if the plant output function is purely a function of the state. Next, using center manifold theory, we derive necessary and sufficient conditions for the existence of general exponential observers for Lyapunov stable nonlinear systems. As an application of this result, we show that for the existence of general exponential observers for Lyapunov stable nonlinear systems, the dimension of the state of the general exponential observer should not be less than the number of critical eigenvalues of the linearization matrix of the state dynamics of the plant.