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The state-space realization of the constant is trivially () = (). Together we then get a state-space realization with matrices A , B and C determined by the strictly proper part, and matrix D determined by the constant.
This state-space realization is called controllable canonical form (also known as phase variable canonical form) because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state).
In control theory, given any transfer function, any state-space model that is both controllable and observable and has the same input-output behaviour as the transfer function is said to be a minimal realization of the transfer function. [1] [2] The realization is called "minimal" because it describes the system with the minimum number of ...
In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.
In more formal probability theory, a random variable is a function X defined from a sample space Ω to a measurable space called the state space. [2] [a] If an element in Ω is mapped to an element in state space by X, then that element in state space is a realization.
In control engineering and other areas of science and engineering, state variables are used to represent the states of a general system. The set of possible combinations of state variable values is called the state space of the system. The equations relating the current state of a system to its most recent input and past states are called the ...
The Eigensystem realization algorithm (ERA) is a system identification technique popular in civil engineering, in particular in structural health monitoring [citation needed]. ERA can be used as a modal analysis technique and generates a system realization using the time domain response (multi-)input and (multi-)output data. [ 1 ]
Hankel matrices are formed when, given a sequence of output data, a realization of an underlying state-space or hidden Markov model is desired. [3] The singular value decomposition of the Hankel matrix provides a means of computing the A , B , and C matrices which define the state-space realization. [ 4 ]