The Experts below are selected from a list of 87 Experts worldwide ranked by ideXlab platform

Chen Naihui - One of the best experts on this subject based on the ideXlab platform.

B. P. Kharlamov - One of the best experts on this subject based on the ideXlab platform.

  • Characteristic operator and the curvilinear integral for a semi-Markov process
    Journal of Soviet Mathematics, 1992
    Co-Authors: B. P. Kharlamov
    Abstract:

    The connection between the characteristic operator and the Lévy representation of the Conditional generating function of the first exit time of a semi-Markov process is considered. The absolutely continuous part of Lévy's additive functional is expressed in the form of a curvilinear integral of the value of the characteristic operator of unity with respect to the Conditional Mathematical Expectation of the traversal time relative to sequences of states. The obtained formula is used for a new derivation of the linearity of the characteristic operator for a Markov process.

  • Characteristic operator and the curvilinear integral for a semi-Markov process
    Journal of Mathematical Sciences, 1992
    Co-Authors: B. P. Kharlamov
    Abstract:

    The connection between the characteristic operator and the Levy representation of the Conditional generating function of the first exit time of a semi-Markov process is considered. The absolutely continuous part of Levy's additive functional is expressed in the form of a curvilinear integral of the value of the characteristic operator of unity with respect to the Conditional Mathematical Expectation of the traversal time relative to sequences of states. The obtained formula is used for a new derivation of the linearity of the characteristic operator for a Markov process.

Kan-jian Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Exponential $H_{\infty}$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2011
    Co-Authors: Feipeng Da, Kan-jian Zhang
    Abstract:

    In this paper, the exponential H∞ filtering problem is studied for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements. The measurement missing phenomenon, which is related to the modes of subsystems, is described in the form of random matrix function and the missing probability of each sensor at every mode is governed by an individual random variable taking values in the interval [0,1] . This description of missing measurements is more general than the existing ones, where the missing probability is described by a Bernoulli distribution white sequence or a certain diagonal matrix. By using Lyapunov method and the properties of Conditional Mathematical Expectation, we propose a novel approach to achieve the delay-dependent exponential stability criterion such that the filtering error system is mean-square exponentially stable and satisfies a prescribed H∞ performance level. Moreover, there is no equation restriction on decay rate. Then, based on the obtained sufficient criterion, the filter matrices can be directly characterized by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the main result.

Feipeng Da - One of the best experts on this subject based on the ideXlab platform.

  • Exponential $H_{\infty}$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2011
    Co-Authors: Feipeng Da, Kan-jian Zhang
    Abstract:

    In this paper, the exponential H∞ filtering problem is studied for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements. The measurement missing phenomenon, which is related to the modes of subsystems, is described in the form of random matrix function and the missing probability of each sensor at every mode is governed by an individual random variable taking values in the interval [0,1] . This description of missing measurements is more general than the existing ones, where the missing probability is described by a Bernoulli distribution white sequence or a certain diagonal matrix. By using Lyapunov method and the properties of Conditional Mathematical Expectation, we propose a novel approach to achieve the delay-dependent exponential stability criterion such that the filtering error system is mean-square exponentially stable and satisfies a prescribed H∞ performance level. Moreover, there is no equation restriction on decay rate. Then, based on the obtained sufficient criterion, the filter matrices can be directly characterized by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the main result.

Weihai Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Robust $H_\infty$ Filtering for Nonlinear Discrete-time Stochastic Systems
    arXiv: Optimization and Control, 2018
    Co-Authors: Tianliang Zhang, Feiqi Deng, Weihai Zhang
    Abstract:

    This paper mainly discusses the $H_{\infty}$ filtering of general nonlinear discrete time-varying stochastic systems. A nonlinear discrete-time stochastic bounded real lemma (SBRL) is firstly obtained by means of the smoothness of the Conditional Mathematical Expectation, and then, based on the given SBRL and a stochastic LaSalle-type theorem, a sufficient condition for the existence of the $H_\infty$ filtering of general nonlinear discrete time-varying stochastic systems is presented via a new introduced Hamilton-Jacobi inequality (HJI), which is easily verified. When the worst-case disturbance $\{v^*_k\}_{k\in {\mathcal N}}$ is considered, the suboptimal $H_2/H_\infty$ filtering is studied. Two examples including a practical engineering example show the effectiveness of our main results.