Topic
State variable
About: State variable is a research topic. Over the lifetime, 14354 publications have been published within this topic receiving 254707 citations.
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01 Jan 1965
TL;DR: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data is presented in this article, where a Markov-parametric algorithm is used to construct the minimal realization.
Abstract: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data
908 citations
TL;DR: A recursive algorithm is developed which calculates a time-varying ellipsoid in state space that always contains the system's true state and is motivated by the problem of tracking an evasive target, but the results have wider applications.
Abstract: A method is discussed for estimating the state of a linear dynamic system using noisy observations, when the input to the dynamic system and the observation errors are completely unknown except for bounds on their magnitude or energy. The state estimate is actually a set in state space rather than a single vector. The optimum estimate is the smallest calculable set which contains the unknown system state, but it is usually impractical to calculate this set. A recursive algorithm is developed which calculates a time-varying ellipsoid in state space that always contains the system's true state. Unfortunately the algorithm is still unproven in the sense that its performance has not yet been evaluated. The algorithm is closely related in structure but not in performance to the algorithm obtained when the system inputs and observation errors are white Gaussian processes. The algorithm development is motivated by the problem of tracking an evasive target, but the results have wider applications.
905 citations
TL;DR: In this paper, the concept of a Lie series is enlarged to encompass the cases where the generating function itself depends explicity on the small parameter, and the formalism generates nonconservative as well as conservative transformations.
Abstract: The concept of a Lie series is enlarged to encompass the cases where the generating function itself depends explicity on the small parameter. Lie transforms define naturally a class of canonical mappings in the form of power series in the small parameter. The formalism generates nonconservative as well as conservative transformations. Perturbation theories based on it offer three substantial advantages: they yield the transformation of state variables in an explicit form; in a function of the original variables, substitution of the new variables consists simply of an iterative procedure involving only explicit chains of Poisson brackets; the inverse transformation can be built the same way.
880 citations
TL;DR: In this paper, an energy-based coupled elastoplastic damage theory for ductile and brittle materials is presented, which employs irreversible thermodynamics and internal state variable theory for damage.
865 citations
TL;DR: A dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model.
853 citations