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State-space representation

About: State-space representation is a research topic. Over the lifetime, 4978 publications have been published within this topic receiving 73054 citations.


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TL;DR: In this paper, a general theory of dissipative dynamical systems is presented, where dissipativeness is defined in terms of an inequality involving the storage function and the supply function, which is bounded from below by the available storage and from above by the required supply.
Abstract: The first part of this two-part paper presents a general theory of dissipative dynamical systems. The mathematical model used is a state space model and dissipativeness is defined in terms of an inequality involving the storage function and the supply function. It is shown that the storage function satisfies an a priori inequality: it is bounded from below by the available storage and from above by the required supply. The available storage is the amount of internal storage which may be recovered from the system and the required supply is the amount of supply which has to be delivered to the system in order to transfer it from the state of minimum storage to a given state. These functions are themselves possible storage functions, i.e., they satisfy the dissipation inequality. Moreover, since the class of possible storage functions forms a convex set, there is thus a continuum of possible storage functions ranging from its lower bound, the available storage, to its upper bound, the required supply. The paper then considers interconnected systems. It is shown that dissipative systems which are interconnected via a neutral interconnection constraint define a new dissipative dynamical system and that the sum of the storage functions of the individual subsystems is a storage function for the interconnected system. The stability of dissipative systems is then investigated and it is shown that a point in the state space where the storage function attains a local minimum defines a stable equilibrium and that the storage function is a Lyapunov function for this equilibrium. These results are then applied to several examples. These concepts and results will be applied to linear dynamical systems with quadratic supply rates in the second part of this paper.

3,124 citations

Journal ArticleDOI
TL;DR: This work shows how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time.
Abstract: SUMMARY We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our approach by several examples and empirically compare its performance to another Gibbs sampler where the states are generated one at a time. The empirical results suggest that our approach is both practical to implement and dominates the Gibbs sampler that generates the states one at a time.

2,146 citations

Journal ArticleDOI
TL;DR: In this paper, the linear time-discrete state-space model is generalized from single-dimensional time to two-dimensional space, which includes extending certain basic known concepts from one to two dimensions, such as the general response formula, state transition matrix, Cayley-Hamilton theorem, observability, and controllability.
Abstract: The linear time-discrete state-space model is generalized from single-dimensional time to two-dimensional space. The generalization includes extending certain basic known concepts from one to two dimensions. These concepts include the general response formula, state-transition matrix, Cayley-Hamilton theorem, observability, and controllability.

1,710 citations

Journal ArticleDOI
TL;DR: In this article, the authors extended Hamilton's Markov-switching model to a general state-space model and proposed a filtering and smoothing algorithm to estimate a broad class of models.

1,456 citations

Journal ArticleDOI
TL;DR: A new approach to automatic business forecasting based on an extended range of exponential smoothing methods that allows the easy calculation of the likelihood, the AIC and other model selection criteria, and the computation of prediction intervals for each method.

873 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202340
2022105
2021157
2020213
2019272
2018279