Sufficient Conditions For Observability Research Articles

General Solution and Observability of Singular Differential Systems with Delay

We study singular differential systems with delay. A general description for the solutions of singular differential systems with delay is given and a necessary and sufficient condition for exact observability of singular differential systems with delay is derived.

Observability and detectability of discrete-time stochastic systems with Markovian jump

This paper studies detectability and observability of Markov jump discrete-time linear stochastic systems with multiplicative noise (MJDLS for short). The relations between some concepts of detectability and observability are established. These relations, together with equivalent expressions of observability Gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability. As applications, discrete-time stochastic Lyapunov equations and stochastic discrete algebraic Riccati equations (SDARE) are discussed.

Observability of nonlinear control systems on time scales

The problem of observability of the family of nonlinear control systems defined on any time scale and parameterised by time instant t 0 is developed. Necessary and sufficient conditions for observability are given. Because time scale is a rich model of time that includes continuous- and discrete-time models as standard cases, the obtained results extend classical observability rank conditions given for continuous-time systems and discrete-time systems.

Structural Observability of Controlled Switching Linear Systems

In this paper, a new methodology for analysis of structural observability of controlled switching linear systems modelled by bond graphs is proposed. Causal man ipulations on the bond graph model enable to determine graphically the observable subspace. A novel definit ion of observability is proposed. Finally, t wo sufficient conditions of observability are derived. The proposed method, based on a bond graph theoretic approach, assumes only the knowledge of the systems structure. These conditions can be implemented by classical bond graph theory algorith ms based on finding particular paths and cycles in a bond graph.

Hybrid‐type observer design based on a sufficient condition for observability in switched nonlinear systems

SUMMARYThis paper presents a sufficient condition for observability of continuous‐time switched nonlinear systems that also involve state jumps. Without the assumption of observability of individual modes, the sufficient condition is based on gathering partial information from each mode so that the state is completely recovered after several switchings. Based on the sufficient condition, a hybrid‐type observer is designed, which comprises a copy of the actual plant and an error correction scheme at discrete time instants. In order to execute the proposed design, the observable component of the state at each mode needs to be estimated without transients or ‘peaking’ (caused by high‐gain observers), and this motivates us to introduce a back‐and‐forth estimation technique. Under the assumption of persistent switching, analysis shows that the estimate thus generated converges asymptotically to the actual state of the system. Simulation results validate the utility of the proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.

Observability Analysis and Improved Zero‐Speed Position Observer Design of Synchronous Motor with Experimental Results

AbstractThis paper deals with the permanent magnet synchronous motor (PMSM) observability analysis for sensorless control design. The problem of loss of observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical observability analyses for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed especially towords the necessary observability condition analysis. Furthermore, improved zero‐speed observation is presented here for a surface PMSM (SPMSM) to overcome position observability problems at zero‐speed which is an unobservable state point. The proposed observer based on higher order sliding mode (HOSM) is designed in order to ensure robustness against disturbances and to avoid the chattering phenomenon which is inherent in standard first order sliding modes. The stability and finite time convergence of the developed observer are studied and discussed. Experimental results are carried out to illustrate the effectiveness and robustness of the proposed observer.

Decentralized Laplacian Eigenvalues Estimation and Collaborative Network Topology Identification

In this paper we first study observability conditions on networks. Based on spectral properties of graphs, we state new sufficient or necessary conditions for observability. These conditions are based on properties of the Khatri-Rao product of matrices. Then we consider the problem of estimating the eigenvalues of the Laplacian matrix associated with the graph modeling the interconnections between the nodes of a given network. Eventually, we extend the study to the identification of the network topology by estimating both eigenvalues and eigenvectors of the network matrix. In addition, we show how computing, in finite-time, some linear functionals of the state initial condition, including average consensus. Specifically, based on properties of the observability matrix, we show that Laplacian eigenvalues can be recovered by solving a local eigenvalue decomposition on an appropriately constructed matrix of observed data. Unlike FFT based methods recently proposed in the literature, in the approach considered herein, we are also able to estimate the multiplicities of the eigenvalues. Then, for identifying the network topology, the eigenvectors are estimated by means of a consensus-based least squares method.

Reduced order dead-beat observers for the chemostat

This paper studies the strong observability property and the reduced-order dead-beat observer design problem for a continuous bioreactor. New relationships between coexistence and strong observability, and checkable sufficient conditions for strong observability, are established for a chemostat with two competing microbial species. Furthermore, the dynamic output feedback stabilization problem is solved for the case of one species.

Sensor location for discrete mode observability of switching linear systems with unknown inputs

This paper deals with the problem of additional sensor placement in order to recover the discrete mode observability of switching structured linear systems with unknown inputs. Such a property is quite important for designing control laws, observers, fault detection and isolation schemes (when the fault occurrence implies a commutation between two modes), and so on. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, new necessary and sufficient conditions for discrete mode generic observability. When these conditions are not satisfied, we propose a sensor placement procedure which allows us to recover the mode observability. Our approach can be implemented by classical and quite simple graph-theory algorithms.

Optimal state estimation of controllable quantum dynamical systems

We present system-theoretic quantum state reconstruction methods that minimize estimation error by combining optimal quantum control with asymptotically efficient estimation. Introducing the notion of optimal observability of a quantum dynamical system---a concept that does not exist in classical control theory---we formulate and solve the Pareto optimal control problem of maximizing state estimation accuracy while minimizing the expenditure of available control and measurement resources. Necessary and sufficient conditions for optimal observability, based on the quantum optimal observability Gramian, are presented. We examine the finite sample efficiency of the estimation methodology for two- and three-level systems using ideal and noisy control fields, and demonstrate the advantages of state reconstruction schemes based on optimal observability theory for experimentally realistic sample sizes. These results indicate that the optimal control of quantum measurement bases can be used to minimize state reconstruction errors by fully exploiting the information geometry of quantum states.

Controllability and observability of impulsive fractional linear time-invariant system

In this paper, we deal with the controllability and observability of impulsive fractional linear time-invariant (IF-LTI for short) system. Our main purpose is to built some necessary and sufficient conditions of controllability and observability for the IF-LTI system. At the same time, we establish some conclusions of controllability and observability for a continuous fractional LTI system, which is a special case of the IF-LTI system. Examples are given to illustrate our results.

Fractional discrete-time linear control systems with initialisation

Linear control systems with fractional differences and finite memory are considered. The evaluation of trajectories of such systems is studied. The extension of the classical notion of observability and controllability is given and developed. The necessary and sufficient conditions for observability and controllability are proved.

Exact observability, square functions and spectral theory

In the first part of this article we introduce the notion of a backward–forward conditioning (BFC) system that generalises the notion of zero-class admissibility introduced in Xu et al. (2008) [30]. We can show that unless the spectrum contains a half-plane, the BFC property occurs only in situations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact and final state observability in Banach spaces that is designed for infinite-dimensional output spaces and general strongly continuous semigroups. To obtain this we make use of certain weighted square function estimates. Specialising to the Hilbert space situation we obtain a result for contraction semigroups without an analyticity condition on the semigroup.

Geometric Analysis of Reachability and Observability for Impulsive Systems on Complex Field

Nowadays, quantum systems have become one of the focuses of the ongoing research and they are typical complex systems, whose state variables are defined on the complex field. In this paper, the issue of reachability and observability is addressed for a class of linear impulsive systems on complex field, for simplicity, complex linear impulsive systems. This kind of time‐driven impulsive systems allows free impulsive instants, which leads to the limitation of using traditional definitions of reachability and observability directly. New notations about the span reachable set and unobservable set are proposed. Sufficient and necessary conditions for span reachability and observability of such systems are established. Moreover, the explicit characterization of span reachable set and unobservable set is presented by geometric analysis. It is pointed out that the geometric conditions are equivalent to the algebraic ones in known results for special cases. Numerical examples are also presented to show the effectiveness of the proposed methods.

A Graph Approach to Observability in Physical Sparse Linear Systems

A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the systems. The term observability refers to the capability of estimating the state variables of a system based on the available information. In the case of linear systems, diffierent graphical approaches were developed to address this issue. In this paper a new unified graph based technique is proposed in order to determine the observability of a sparse linear physical system or, at least, a system that can be linearized after a first order derivative, using a given sensor set. A network associated to a linear equation system is introduced, which allows addressing and solving three related problems: the characterization of those cases for which algebraic and topological observability analysis return contradictory results; the characterization of a necessary and sufficient condition for topological observability; the determination of the maximum observable subsystem in case of unobservability. Two examples illustrate the developed techniques.

Controllability and observability of switched linear systems with continuous-time and discrete-time subsystems

In this study, the authors focus on the controllability and observability of switched linear systems composed by continuous-time and discrete-time subsystems. Necessary and sufficient conditions for controllability and observability are obtained. A simple example is proposed to illustrate the effectiveness of the current theoretical results.

Observability analysis of Boolean control networks with impulsive effects

The observability for the Boolean control networks with impulsive effects is discussed. After a brief introduction on converting the Boolean control networks with impulsive effects into impulsive discrete-time systems, necessary and sufficient conditions of observability for the Boolean control networks with impulsive effects are obtained. Finally, an example is presented to show the effectiveness of the proposed results.

Conditions for distinguishability and observability of switched linear systems

A characterization for weak distinguishability of two linear controlled systems are derived. In addition, the observability of a special switched linear controlled system is considered, and necessary and sufficient conditions for observability are obtained.

On controllability and observability for a class of linear impulsive dynamic systems on time scales

The aim of this paper is to study the controllability and observability for a class of linear time-varying impulsive control systems on time scales. Sufficient and necessary conditions for state controllability and state observability of such systems are established. The corresponding criteria for time-invariant impulsive control systems on time scales are also obtained.

Array Shape Observability From Time Differences of Arrival

In this paper, we study the observability conditions for the relative position of a set of passive sensors from the measured time differences of arrival (TDOA) of signals from a set of noncooperative sources lying in the same plane. The sources are broadband to measure the TDOA and far enough to consider each source is detected in the same line of sight by each sensor. We show that a necessary observability condition is to have at least three sensors and three sources. Then, the sufficient observability conditions are established in this minimal configuration. Finally, we propose an algorithm to compute both sensors' location and the direction of arrival (DOA) of the sources, from the noise-free TDOA.