State Space Model
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State space models linear time invariant lti state space models are a linear representation of a dynamic system in either discrete or continuous time.
State space model. A is the system matrix. A state space model is a mathematical representation of a physical system as a set of input output and state variables related by first order differential equations. Putting a model into state space form is the basis for many methods in process dynamics and control analysis. A state space model is a discrete time stochastic model that contains two sets of equations.
One describing how a latent process transitions in time the state equation another describing how an observer measures the latent process at each period the observation equation. Y cx du. The ss model object can represent siso or mimo state space models in continuous time or discrete time. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables.
In continuous time a descriptor state space model takes the following form. The first and the second equations are known as state equation and output equation respectively. The state variables define the values of the output variables. The true power of the state space model is to allow the creation and estimation of custom models.
E d x d t a x b u y c x d u where x is the state vector. U is the input vector and y is the output vector. The state space model of linear time invariant lti system can be represented as x ax bu. Usually that is done by extending the following two classes which bundle all of state space representation kalman filtering and maximum likelihood fitting functionality for estimation and results output.
State variables x t can be reconstructed from the measured input output data but are not themselves measured during an experiment. U and y are input vector and output vector respectively. Below is the continuous time form of a model in state space form. A descriptor state space model is a generalized form of state space model.
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