A spectral test for observability and detectability of discrete-time linear time-varying systems

Peters, Marc A.; Iglesias, Pablo A.

doi:10.1109/cdc.1997.652475

Cited by 8 publications

(4 citation statements)

References 5 publications

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“…(ii) Following the line of [35] that transforms the system (3) into a deterministic time-varying system, it is easy to give some testing criteria for uniform detectability and observability of (3) by means of the existing results on deterministic time-varying systems [23]. In addition, applying the infinitedimensional operator theory, the spectral criterion for stability of system (3) is also a valuable research issue.…”

Section: Additional Commentsmentioning

confidence: 99%

“…In [19], the exact detectability in [36] and detectability in [6] were proved to be equivalent, and a unified treatment was proposed for detectability and observability of Itô stochastic systems. Based on the standard notions of detectability and observability for time-varying linear systems [1], [23], studied in [20] were detectability and observability of discrete time-invariant stochastic systems as well as the properties of Lyapunov equations. Recently, the exact detectability and observability were extended to stochastic systems with Markov jumps and multiplicative noise in [5], [22], [27], [37].…”

Section: Introductionmentioning

confidence: 99%

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Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Zhang

Zheng

Chen

2016

International Journal of Control

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The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, K ∞ -exact detectability (resp. K W F T -exact detectability, K F T -exact detectability, K N -exact detectability) and K ∞ -exact observability (resp. K W F T -exact observability, K F T -exact observability, K N -exact observability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalized Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, K N -exact observability and K N -exact detectability, respectively.

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Section: Additional Commentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Zhang

Zheng

Chen

2016

International Journal of Control

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“…They include a characterization of stability, observability and detectability properties for linear time-varying difference equations (cf. [27,40,51] and the references therein) in terms of spectral properties for matrix-or operator-weighted shifts. For instance, [27,Thm 4.5] show that a nonautonomous linear difference equation…”

Section: Nonautonomous Hyperbolicitymentioning

confidence: 99%

Fine Structure of the Dichotomy Spectrum

Pötzsche

2012

Integr. Equ. Oper. Theory

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The dichotomy spectrum is a crucial notion in the theory of dynamical systems, since it contains information on stability and robustness properties. However, recent applications in nonautonomous bifurcation theory showed that a detailed insight into the fine structure of this spectral notion is necessary. On this basis, we explore a helpful connection between the dichotomy spectrum and operator theory. It relates the asymptotic behavior of linear nonautonomous difference equations to the point, surjectivity and Fredholm spectra of weighted shifts. This link yields several dynamically meaningful subsets of the dichotomy spectrum, which not only allows to classify and detect bifurcations, but also simplifies proofs for results on the long term behavior of difference equations with explicitly time-dependent right-hand side.

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“…Then the system is called N-step observable if, and only if, its observation matrix M satisfies (Peters andIglesias, 1997 andBar-Shalom, 2001):…”

Section: O P T I M I Z E D B I a S E S T I M At I O N M O D E Lmentioning

confidence: 99%

Optimized Bias Estimation Model for Mobile Radar Error Registration

et al. 2012

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For mobile 3-D radar installed on a gyro-stabilized platform, its measurements are usually contaminated by the systematic biases which contain radar offset biases (i.e., range, azimuth and elevation biases) and attitude biases (i.e., yaw, pitch and roll biases) of the platform because of the errors in the Inertial Measurement Units (IMU). Systematic biases can NOT be removed by a single radar itself; however, fortunately, they can be estimated by using two different radar measurements of the same target. The process of estimating systematic biases and then compensating radar measurements is called error registration. In this paper, the registration models are established first, then, the equivalent radar measurement error expressions caused by the attitude biases are derived and the dependencies among attitude biases and offset biases are analysed by using the observable matrix criterion. Based on the analyses above, an Optimized Bias Estimation Model (OBEM) is proposed for registration. OBEM uses the subtraction of azimuth and yaw bias as one variable and omits roll and pitch biases in the state vector, which decreases the dimension of the state vector from fourteen of the All Augmented Model (AAM), (which uses all the systematic biases of both radars as state vector) to eight and has about 80% reduction in calculation costs. Also, OBEM can decrease the coupling influences of roll and pitch biases and improve the estimation performance of radar elevation bias. Monte Carlo experiments were made. Numerical results showed that the bias estimation accuracies and the rectified radar raw measurement accuracies can be improved. K E Y WO R D S1. Error Registration.2. Attitude Bias. 3. All Augmented Model (AAM). 4. Optimized Bias Estimation Model (OBEM).

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A spectral test for observability and detectability of discrete-time linear time-varying systems

Cited by 8 publications

References 5 publications

Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Fine Structure of the Dichotomy Spectrum

Optimized Bias Estimation Model for Mobile Radar Error Registration

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