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Tomomichi Hagiwara - One of the best experts on this subject based on the ideXlab platform.
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properties of discrete time Noncausal linear periodically time varying scaling and their relationship with shift invariance in lifting timing
International Journal of Control, 2011Co-Authors: Yohei Hosoe, Tomomichi HagiwaraAbstract:This article is concerned with the technique called discrete-time Noncausal linear periodically time-varying (LPTV) scaling for robust stability analysis. Noncausal LPTV scaling has already been shown to be effective for reducing the conservativeness of robustness analysis in theoretical and numerical ways. However, there still remain some issues to be resolved for further understanding and exploiting Noncausal LPTV scaling, e.g. its relationship with the conventional analysis approach of causal linear time-invariant scaling. In this article, by introducing the key idea of shift-invariance in lifting-timing, we discuss the difference and corresponding relationship between the conventional approach and Noncausal LPTV scaling.
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research article properties of discrete time Noncausal linear periodically time varying scaling and their relationship with shift invariance in lifting timing
2011Co-Authors: Yohei Hosoe, Tomomichi HagiwaraAbstract:This paper is concerned with the technique called discrete-time Noncausal linear periodically time-varying (LPTV) scaling for robust stability analysis. Noncausal LPTV scaling has already been shown to be effective for reducing the conservativeness of robustness analysis in theoretical and numerical ways. However, there still remain some issues to be resolved for further understanding and exploiting Noncausal LPTV scaling, e.g., its relationship with the conventional analysis approach of causal linear time-invariant scaling. In this paper, by introducing the key idea of shift-invariance in lifting-timing, we discuss the difference and corresponding relationship between the conventional approach and Noncausal LPTV scaling. In this paper, we discuss the properties of discrete-time Noncausal linear periodically time-varying (LPTV) scaling (Hagiwara and Ohara 2007, 2010), which is an approach to the robustness analysis of discrete-time linear time-invariant (LTI) and LPTV systems. The famous lifting technique (Bittanti and Colaneri 2000, 2009) enables us to treat discrete-time LPTV systems as if they were LTI. Hence, given an LPTV system (or an LTI system as a special case), we can analyze its robust stability by applying the separator-type robust stability theorem (Iwasaki and Hara 1998) to the lifted LTI system. Noncausal LPTV scaling is an idea that can be introduced quite naturally in such an analysis by allowing some Noncausal operations of signals through the lifted treatment. Noncausality thus introduced in the scaling approach has been demonstrated to be effective for reducing the conservativeness in the robustness analysis of LTI and LPTV systems, both theoretically and numerically (Hagiwara and Ohara 2007, 2010). In particular, as far as LTI systems are concerned, it has been proved that even if we confine ourselves to static Noncausal LPTV scaling, it induces some dynamic causal LTI scaling when it is interpreted in the lifting-free (i.e., conventional) treatment. This property endows (even static) Noncausal LPTV scaling with a promising ability in achieving less conservative analysis, in spite of its simple treatment. Such a feature of Noncausal LPTV scaling has already been exploited also in the development of robust controller synthesis methods (Hosoe and Hagiwara 2010a,b), and their effectiveness in comparison with the µ-synthesis (Zhou and Doyle 1998) has also been confirmed. Despite the promising properties on the practical side of Noncausal LPTV scaling described above as a new approach to robust control, however, its comprehensive properties have not necessarily been revealed entirely. The missing arguments include, e.g., the characterization of the class of dynamic causal LTI scaling in the lifting-free treatment that can equivalently be dealt with by working instead on static Noncausal LPTV scaling in the lifted treatment; or what theoretical differences there are between Noncausal LPTV scaling and the conventional causal
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relationship between Noncausal linear periodically time varying scaling and causal linear time invariant scaling for discrete time systems
IFAC Proceedings Volumes, 2011Co-Authors: Yohei Hosoe, Tomomichi HagiwaraAbstract:Abstract In this paper, we discuss the relationship between Noncausal linear periodically time-varying (LPTV) scaling and causal linear time-invariant (LTI) scaling against discrete-time LTI closed-loop system. Noncausal LPTV scaling is naturally introduced via lifting technique, and can induce some frequency-dependent scaling in the lifting-free (i.e., usual) framework. However, it has not been clear what classes of Noncausal LPTV scaling and causal LTI scaling have equivalent abilities in their respective frameworks. It is an important issue for sophisticating the theoretical base of Noncausal LPTV scaling, and this paper studies such a relationship.
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brief paper Noncausal linear periodically time varying scaling for robust stability analysis of discrete time systems frequency dependent scaling induced by static separators
Automatica, 2010Co-Authors: Tomomichi Hagiwara, Yasuhiro OharaAbstract:This article is concerned with robust stability analysis of discrete-time systems and introduces a novel and powerful technique that we call Noncausal linear periodically time-varying (LPTV) scaling. Based on the discrete-time lifting together with the conventional but general scaling approach, we are led to the notion of Noncausal LPTV scaling for LPTV systems, and its effectiveness is demonstrated with a numerical example. To separate the effect of Noncausal and LPTV characteristics of Noncausal LPTV scaling to see which is a more important source leading to the effectiveness, we then consider the case of LTI systems as a special case. Then, we show that even static Noncausal LPTV scaling has an ability of inducing frequency-dependent scaling when viewed in the context of the conventional LTI scaling, while causal LPTV scaling fails to do so. It is further discussed that the effectiveness of Noncausal characteristics leading to the frequency-domain interpretation can be exploited even for LPTV systems by considering the @nN-lifted transfer matrices of N-periodic systems.
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robust stability analysis of sampled data systems with Noncausal periodically time varying scaling optimization of scaling via approximate discretization and error bound analysis
Conference on Decision and Control, 2007Co-Authors: Tomomichi Hagiwara, Hiroaki UmedaAbstract:A novel idea called Noncausal linear periodically time-varying (LPTV) scaling has been proposed for robust stability analysis of sampled-data systems. This paper gives a method for approximately optimizing Noncausal LPTV scaling by establishing a link between the Noncausal LPTV scaling of sampled-data systems and the conventional scaling of discrete- time systems. More precisely, applying what we call the fast- lifting technique, we derive a discrete-time system that is approximately equivalent to the sampled-data system with respect to the optimization of scaling parameters. We further give a method for computing an upper bound of the associated approximation error, together with a few methods for obtaining reduced error bounds. We then demonstrate the effectiveness of Noncausal LPTV scaling through numerical examples.
Yohei Hosoe - One of the best experts on this subject based on the ideXlab platform.
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properties of discrete time Noncausal linear periodically time varying scaling and their relationship with shift invariance in lifting timing
International Journal of Control, 2011Co-Authors: Yohei Hosoe, Tomomichi HagiwaraAbstract:This article is concerned with the technique called discrete-time Noncausal linear periodically time-varying (LPTV) scaling for robust stability analysis. Noncausal LPTV scaling has already been shown to be effective for reducing the conservativeness of robustness analysis in theoretical and numerical ways. However, there still remain some issues to be resolved for further understanding and exploiting Noncausal LPTV scaling, e.g. its relationship with the conventional analysis approach of causal linear time-invariant scaling. In this article, by introducing the key idea of shift-invariance in lifting-timing, we discuss the difference and corresponding relationship between the conventional approach and Noncausal LPTV scaling.
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research article properties of discrete time Noncausal linear periodically time varying scaling and their relationship with shift invariance in lifting timing
2011Co-Authors: Yohei Hosoe, Tomomichi HagiwaraAbstract:This paper is concerned with the technique called discrete-time Noncausal linear periodically time-varying (LPTV) scaling for robust stability analysis. Noncausal LPTV scaling has already been shown to be effective for reducing the conservativeness of robustness analysis in theoretical and numerical ways. However, there still remain some issues to be resolved for further understanding and exploiting Noncausal LPTV scaling, e.g., its relationship with the conventional analysis approach of causal linear time-invariant scaling. In this paper, by introducing the key idea of shift-invariance in lifting-timing, we discuss the difference and corresponding relationship between the conventional approach and Noncausal LPTV scaling. In this paper, we discuss the properties of discrete-time Noncausal linear periodically time-varying (LPTV) scaling (Hagiwara and Ohara 2007, 2010), which is an approach to the robustness analysis of discrete-time linear time-invariant (LTI) and LPTV systems. The famous lifting technique (Bittanti and Colaneri 2000, 2009) enables us to treat discrete-time LPTV systems as if they were LTI. Hence, given an LPTV system (or an LTI system as a special case), we can analyze its robust stability by applying the separator-type robust stability theorem (Iwasaki and Hara 1998) to the lifted LTI system. Noncausal LPTV scaling is an idea that can be introduced quite naturally in such an analysis by allowing some Noncausal operations of signals through the lifted treatment. Noncausality thus introduced in the scaling approach has been demonstrated to be effective for reducing the conservativeness in the robustness analysis of LTI and LPTV systems, both theoretically and numerically (Hagiwara and Ohara 2007, 2010). In particular, as far as LTI systems are concerned, it has been proved that even if we confine ourselves to static Noncausal LPTV scaling, it induces some dynamic causal LTI scaling when it is interpreted in the lifting-free (i.e., conventional) treatment. This property endows (even static) Noncausal LPTV scaling with a promising ability in achieving less conservative analysis, in spite of its simple treatment. Such a feature of Noncausal LPTV scaling has already been exploited also in the development of robust controller synthesis methods (Hosoe and Hagiwara 2010a,b), and their effectiveness in comparison with the µ-synthesis (Zhou and Doyle 1998) has also been confirmed. Despite the promising properties on the practical side of Noncausal LPTV scaling described above as a new approach to robust control, however, its comprehensive properties have not necessarily been revealed entirely. The missing arguments include, e.g., the characterization of the class of dynamic causal LTI scaling in the lifting-free treatment that can equivalently be dealt with by working instead on static Noncausal LPTV scaling in the lifted treatment; or what theoretical differences there are between Noncausal LPTV scaling and the conventional causal
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relationship between Noncausal linear periodically time varying scaling and causal linear time invariant scaling for discrete time systems
IFAC Proceedings Volumes, 2011Co-Authors: Yohei Hosoe, Tomomichi HagiwaraAbstract:Abstract In this paper, we discuss the relationship between Noncausal linear periodically time-varying (LPTV) scaling and causal linear time-invariant (LTI) scaling against discrete-time LTI closed-loop system. Noncausal LPTV scaling is naturally introduced via lifting technique, and can induce some frequency-dependent scaling in the lifting-free (i.e., usual) framework. However, it has not been clear what classes of Noncausal LPTV scaling and causal LTI scaling have equivalent abilities in their respective frameworks. It is an important issue for sophisticating the theoretical base of Noncausal LPTV scaling, and this paper studies such a relationship.
Yasuhiro Ohara - One of the best experts on this subject based on the ideXlab platform.
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brief paper Noncausal linear periodically time varying scaling for robust stability analysis of discrete time systems frequency dependent scaling induced by static separators
Automatica, 2010Co-Authors: Tomomichi Hagiwara, Yasuhiro OharaAbstract:This article is concerned with robust stability analysis of discrete-time systems and introduces a novel and powerful technique that we call Noncausal linear periodically time-varying (LPTV) scaling. Based on the discrete-time lifting together with the conventional but general scaling approach, we are led to the notion of Noncausal LPTV scaling for LPTV systems, and its effectiveness is demonstrated with a numerical example. To separate the effect of Noncausal and LPTV characteristics of Noncausal LPTV scaling to see which is a more important source leading to the effectiveness, we then consider the case of LTI systems as a special case. Then, we show that even static Noncausal LPTV scaling has an ability of inducing frequency-dependent scaling when viewed in the context of the conventional LTI scaling, while causal LPTV scaling fails to do so. It is further discussed that the effectiveness of Noncausal characteristics leading to the frequency-domain interpretation can be exploited even for LPTV systems by considering the @nN-lifted transfer matrices of N-periodic systems.
Nikhil Balram - One of the best experts on this subject based on the ideXlab platform.
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Noncausal gauss markov random fields parameter structure and estimation
IEEE Transactions on Information Theory, 1993Co-Authors: Nikhil Balram, Jose M F MouraAbstract:The parameter structure of Noncausal homogeneous Gauss Markov random fields (GMRF) defined on finite lattices is studied. For first-order (nearest neighbor) and a special class of second-order fields, a complete characterization of the parameter space and a fast implementation of the maximum likelihood estimator of the field parameters are provided. For general higher order fields, tight bounds for the parameter space are presented and an efficient procedure for ML estimation is described. Experimental results illustrate the application of the approach presented and the viability of the present method in fitting Noncausal models to 2-D data. >
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recursive structure of Noncausal gauss markov random fields
IEEE Transactions on Information Theory, 1992Co-Authors: Jose M F Moura, Nikhil BalramAbstract:An approach is developed for Noncausal Gauss-Markov random fields (GMRFs) that enables the use of recursive procedures while retaining the Noncausality of the field. Recursive representations are established that are equivalent to the original field. This is achieved by first presenting a canonical representation for GMRFs that is based on the inverse of the covariance matrix, which is called the potential matrix. It is this matrix rather than the field covariance that reflects in a natural way the MRF structure. From its properties, two equivalent one-sided representations are derived, each of which is obtained as the successive iterates of a Riccati-type equation. For homogeneous fields, these unilateral descriptions are symmetrized versions of each other, the study of only one Riccati equation being required. It is proven that this Riccati equation converges at a geometric rate, therefore the one-sided representations are asymptotically invariant. These unilateral representations make it possible to process the fields with well-known recursive techniques such as Kalman-Bucy filters and two-point smoothers. >
Jose M F Moura - One of the best experts on this subject based on the ideXlab platform.
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Noncausal gauss markov random fields parameter structure and estimation
IEEE Transactions on Information Theory, 1993Co-Authors: Nikhil Balram, Jose M F MouraAbstract:The parameter structure of Noncausal homogeneous Gauss Markov random fields (GMRF) defined on finite lattices is studied. For first-order (nearest neighbor) and a special class of second-order fields, a complete characterization of the parameter space and a fast implementation of the maximum likelihood estimator of the field parameters are provided. For general higher order fields, tight bounds for the parameter space are presented and an efficient procedure for ML estimation is described. Experimental results illustrate the application of the approach presented and the viability of the present method in fitting Noncausal models to 2-D data. >
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recursive structure of Noncausal gauss markov random fields
IEEE Transactions on Information Theory, 1992Co-Authors: Jose M F Moura, Nikhil BalramAbstract:An approach is developed for Noncausal Gauss-Markov random fields (GMRFs) that enables the use of recursive procedures while retaining the Noncausality of the field. Recursive representations are established that are equivalent to the original field. This is achieved by first presenting a canonical representation for GMRFs that is based on the inverse of the covariance matrix, which is called the potential matrix. It is this matrix rather than the field covariance that reflects in a natural way the MRF structure. From its properties, two equivalent one-sided representations are derived, each of which is obtained as the successive iterates of a Riccati-type equation. For homogeneous fields, these unilateral descriptions are symmetrized versions of each other, the study of only one Riccati equation being required. It is proven that this Riccati equation converges at a geometric rate, therefore the one-sided representations are asymptotically invariant. These unilateral representations make it possible to process the fields with well-known recursive techniques such as Kalman-Bucy filters and two-point smoothers. >
