Search results for "Filtering problem"
showing 10 items of 11 documents
Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities
2010
In this article, the fault detection (FD) problem for a class of discrete-time Markov jump linear system (MJLS) with partially known transition probabilities is investigated. The proposed systems are more general, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be completely known. A residual generator is constructed and the corresponding FD is formulated as an H ∞ filtering problem by which the error between residual and fault are minimised in the H ∞ sense. The linear matrix inequality-based sufficient conditions for the existence of FD filter are derived. A numerical example on a multiplier–accelerator model economic system is give…
Digital signal processing for relaxation data conversion
2005
Abstract The origins, philosophy and basic practical aspects are considered for an approach of digital data transformations for broadband dielectric relaxation spectroscopy and other relaxation experiments carrying out direct and inverse integral transforms with kernels depending on the ratio or product of arguments. The approach is based on the concept that the mentioned data transformations represent a filtering problem on a logarithmic scale allowing one to implement the transforms by digital functional filters with the logarithmic sampling. As an example, digital Kramers–Kronig transformers are considered.
Finite-Time Hâ Filtering for T-S Fuzzy Discrete-Time Systems with Time-Varying Delay and Norm-Bounded Uncertainties
2015
In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are propose…
Robust L1 fixed-order filtering for switched LPV systems with parameter-dependent delays
2015
Abstract This paper is concerned with the L1 fixed-order filtering problem for a class of switched linear parameter-varying (LPV) systems in which the system matrices and the time delays are dependent on the real-time measured parameters. The authors׳ attention is concentrated on designing the fixed-order filter that guarantees the filtering error system to be exponentially stable and to satisfy a prescribed L1 disturbance attenuation level with respect to all amplitude-bounded disturbances. Based on the switching logic with the minimum average dwell time (ADT), the delay-dependent L1 performance criterion for the switched LPV systems is first established. As there exists coupling between a…
A new design of H ∞ filtering for continuous-time Markovian jump systems with time-varying delay and partially accessible mode information
2013
In this paper, the delay-dependent H"~ filtering problem for a class of continuous-time Markovian jump linear systems with time-varying delay and partially accessible mode information is investigated by an indirect approach. The generality lies in that the systems under consideration are subject to a Markov stochastic process with exactly known and partially unknown transition rates. By utilizing the model transformation idea, an input-output approach is employed to transform the time-delayed filtering error system into a feedback interconnection formulation. Invoking the results from the scaled small gain theorem, an improved version of bounded real lemma is obtained based on a Markovian L…
FIR Kramers–Kronig transformers for relaxation data conversion
2006
It is shown that relaxation data conversion by the Kramers-Kronig (KK) relations can be treated as a filtering problem of band-unlimited relaxation signals in the Mellin transform domain. Based on this concept, KK relations are implemented in the form of FIR filters with the logarithmic sampling. It is demonstrated that KK transformers have sampling rate dependent impulse and frequency responses and only calculation of the imaginary part from the real part can be implemented by a computationally realisable filter. The performance of different types of transformers is studied.Approximately inversely proportional relationship is established between the error and the frequency range of input s…
Digital estimators of relaxation spectra
2007
Determination of the distribution of relaxation times (DRT) from a wide variety of the time- and the frequency-domain material functions, such as polarization current and charge, real and imaginary parts of complex dielectric permittivity and complex dielectric modulus, the appropriate mechanical and magnetic counterparts is generalized as a filtering problem on a logarithmic time or frequency scale. Algorithms of the appropriate digital DRT estimators are derived. A novel regularization strategy is proposed based on choosing sampling rate for the input data, which ensures acceptably low random error of the recovered spectra. Optimum frequency ranges and sampling rates are found for determi…
Robust Estimation for Discrete Markov System with Time-Varying Delay and Missing Measurements
2013
This paper addresses theℋ∞filtering problem for time-delayed Markov jump systems (MJSs) with intermittent measurements. Within network environment, missing measurements are taken into account, since the communication channel is supposed to be imperfect. A Bernoulli process is utilized to describe the phenomenon of the missing measurements. The original system is transformed into an input-output form consisting of two interconnected subsystems. Based on scaled small gain (SSG) theorem and proposed Lyapunov-Krasovskii functional (LKF), the scaled small gains of the subsystems are analyzed, respectively. New conditions for the existence of theℋ∞filters are established, and the correspondingℋ∞f…
Deconvolution filtering for nonlinear stochastic systems with randomly occurring sensor delays via probability-dependent method
2013
This paper deals with a robustH∞deconvolution filtering problem for discrete-time nonlinear stochastic systems with randomly occurring sensor delays. The delayed measurements are assumed to occur in a random way characterized by a random variable sequence following the Bernoulli distribution with time-varying probability. The purpose is to design anH∞deconvolution filter such that, for all the admissible randomly occurring sensor delays, nonlinear disturbances, and external noises, the input signal distorted by the transmission channel could be recovered to a specified extent. By utilizing the constructed Lyapunov functional relying on the time-varying probability parameters, the desired su…
H<inf>&#x221E;</inf> filter design for time-delay Markovian jump systems
2013
This paper investigates the H ∞ filtering problem for discrete time-delay Markovian jump systems with application to networked control systems. To design a full-order filter which ensures the stochastic stability and a prescribed H ∞ performance level for the filtering error system, the Scaled Small Gain (SSG) Theorem is developed for stochastic systems. By employing a two-term approximation to delayed state variables, the original system is transformed into an input-output form consisting of two subsystems. Based on the developed SSG Theorem and the proposed Lyapunov-Krasovskii Functional (LKF), the scaled small gains of the subsystems are analyzed to establish a new condition for the exis…