The Experts below are selected from a list of 58383 Experts worldwide ranked by ideXlab platform
Hamid Reza Karimi - One of the best experts on this subject based on the ideXlab platform.
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new approach to delay dependent h control for continuous time markovian jump systems with time varying delay and deficient transition descriptions
Journal of The Franklin Institute-engineering and Applied Mathematics, 2015Co-Authors: Jianbin Qiu, Yanling Wei, Hamid Reza KarimiAbstract:Abstract This paper proposes an input–output (IO) approach to the delay-dependent stability analysis and H ∞ controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs). The concerned systems are with a time-varying delay in the state and deficient mode information in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-Term Approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO model. Then, based on a Markovian Lyapunov–Krasovskii formulation of SSG condition together with some convexification techniques, the stability analysis and state-feedback H ∞ controller synthesis conditions for the underlying MJLSs are formulated in Terms of linear matrix inequalities. Simulation studies are provided to illustrate the effectiveness and superiority of the proposed analysis and design methods.
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finite time stability analysis and stabilization for linear discrete time system with time varying delay
Journal of The Franklin Institute-engineering and Applied Mathematics, 2014Co-Authors: Zhuo Zhang, Zexu Zhang, Hui Zhang, Bo Zheng, Hamid Reza KarimiAbstract:Abstract The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-Term Approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in Terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.
Hui Zhang - One of the best experts on this subject based on the ideXlab platform.
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finite time stability analysis and stabilization for uncertain continuous time system with time varying delay
Journal of The Franklin Institute-engineering and Applied Mathematics, 2015Co-Authors: Zhuo Zhang, Zexu Zhang, Hui ZhangAbstract:Abstract The problem of finite-time stability for a class of continuous-time system with norm-bounded uncertainties and time-varying delay is studied in this paper. The original system is firstly transformed into two interconnected subsystems. In order to extract the time-varying Term of time delay, a two-Term Approximation of time-varying delay is used. By using the delay-dependent Lyapunov–Krasovskii-like functional and the method of linear matrix inequality (LMI), sufficient conditions for finite-time stability are derived. The derived conditions can analyze the finite-time stability of system and calculate the upper bound of time delay. In order to stabilize unstable system, the state-feedback and output-feedback controller are respectively designed. Results of numerical examples show the effectiveness of the proposed approach.
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finite time stability analysis and stabilization for linear discrete time system with time varying delay
Journal of The Franklin Institute-engineering and Applied Mathematics, 2014Co-Authors: Zhuo Zhang, Zexu Zhang, Hui Zhang, Bo Zheng, Hamid Reza KarimiAbstract:Abstract The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-Term Approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in Terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.
Reinhold Schneider - One of the best experts on this subject based on the ideXlab platform.
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best n Term Approximation in electronic structure calculations ii jastrow factors
Mathematical Modelling and Numerical Analysis, 2007Co-Authors: Heinzjurgen Flad, Wolfgang Hackbusch, Reinhold SchneiderAbstract:We present a novel application of best N -Term Approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best N -Term Approximation spaces , we prove that for q>1 and with respect to a certain class of anisotropic wavelet tensor product bases. Computational arguments are given in favour of this specific class compared to other possible tensor product bases. Finally, we compare the Approximation properties of wavelet bases with standard Gaussian-type basis sets frequently used in quantum chemistry.
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best n Term Approximation in electronic structure calculations i one electron reduced density matrix
Mathematical Modelling and Numerical Analysis, 2006Co-Authors: Heinzjurgen Flad, Wolfgang Hackbusch, Reinhold SchneiderAbstract:We discuss best N -Term Approximation spaces for one-electron wavefunctions and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The Approximation spaces for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in Terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted spaces of wavelet coefficients to proof that both and ρ are in for all with . Our proof is based on the assumption that the possess an asymptotic smoothness property at the electron-nuclear cusps.
Zhuo Zhang - One of the best experts on this subject based on the ideXlab platform.
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finite time stability analysis and stabilization for uncertain continuous time system with time varying delay
Journal of The Franklin Institute-engineering and Applied Mathematics, 2015Co-Authors: Zhuo Zhang, Zexu Zhang, Hui ZhangAbstract:Abstract The problem of finite-time stability for a class of continuous-time system with norm-bounded uncertainties and time-varying delay is studied in this paper. The original system is firstly transformed into two interconnected subsystems. In order to extract the time-varying Term of time delay, a two-Term Approximation of time-varying delay is used. By using the delay-dependent Lyapunov–Krasovskii-like functional and the method of linear matrix inequality (LMI), sufficient conditions for finite-time stability are derived. The derived conditions can analyze the finite-time stability of system and calculate the upper bound of time delay. In order to stabilize unstable system, the state-feedback and output-feedback controller are respectively designed. Results of numerical examples show the effectiveness of the proposed approach.
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finite time stability analysis and stabilization for linear discrete time system with time varying delay
Journal of The Franklin Institute-engineering and Applied Mathematics, 2014Co-Authors: Zhuo Zhang, Zexu Zhang, Hui Zhang, Bo Zheng, Hamid Reza KarimiAbstract:Abstract The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-Term Approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in Terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.
Jianbin Qiu - One of the best experts on this subject based on the ideXlab platform.
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new approach to delay dependent h control for continuous time markovian jump systems with time varying delay and deficient transition descriptions
Journal of The Franklin Institute-engineering and Applied Mathematics, 2015Co-Authors: Jianbin Qiu, Yanling Wei, Hamid Reza KarimiAbstract:Abstract This paper proposes an input–output (IO) approach to the delay-dependent stability analysis and H ∞ controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs). The concerned systems are with a time-varying delay in the state and deficient mode information in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-Term Approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO model. Then, based on a Markovian Lyapunov–Krasovskii formulation of SSG condition together with some convexification techniques, the stability analysis and state-feedback H ∞ controller synthesis conditions for the underlying MJLSs are formulated in Terms of linear matrix inequalities. Simulation studies are provided to illustrate the effectiveness and superiority of the proposed analysis and design methods.
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new approach to delay dependent h α filtering for discrete time markovian jump systems with time varying delay and incomplete transition descriptions
Iet Control Theory and Applications, 2013Co-Authors: Yanling Wei, Mao Wang, Jianbin QiuAbstract:This study is concerned with the delay-dependent H ∞ filter design for a class of discrete-time Markovian jump linear systems (MJLSs) with time-varying delay and incomplete transition descriptions. The considered systems with incomplete transition descriptions cover the MJLSs with known transition probabilities (TPs), partially unknown TPs and uncertain TPs, which are more general. A new equivalent model is proposed for the original MJLSs by employing a two-Term Approximation method, which formulates the filtering problem in the framework of input–output stability. Based on a Markovian Lyapunov–Krasovskii functional combined with the scaled small gain theorem, a new delay-dependent bounded real lemma for the underlying systems is established. It is shown that by using a linearisation technique, the corresponding full- and reduced-order H ∞ filter design is cast into a convex optimisation problem in Terms of linear matrix inequalities. Finally, simulation examples are provided to illustrate the effectiveness and less conservatism of the proposed approach.
