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Every local Noetherian ring admits a system of parameters. [1] It is not possible for fewer than d elements to generate an ideal whose radical is m because then the dimension of R would be less than d. If M is a k-dimensional module over a local ring, then x 1, ..., x k is a system of parameters for M if the length of M / (x 1, ..., x k) M is ...
That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics , computer programming , engineering , statistics , logic , linguistics , and electronic ...
In the context of nonlinear system identification Jin et al. [9] describe grey-box modeling by assuming a model structure a priori and then estimating the model parameters. Parameter estimation is relatively easy if the model form is known but this is rarely the case.
An output parameter, also known as an out parameter or return parameter, is a parameter used for output, rather than the more usual use for input. Using call by reference parameters, or call by value parameters where the value is a reference, as output parameters is an idiom in some languages, notably C and C++, [ b ] while other languages have ...
Since the controller parameters are typically matched to the process characteristics and the process may change, it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics. Moreover, the sensitivity function is also important to analyse how disturbances ...
In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are systems described by partial differential equations or by delay differential equations.
The parameter is not known but its evolution is measured in real time and used for control. If the above equation of parameter dependent system is linear in time then it is called Linear Parameter Dependent systems. They are written similar to Linear Time Invariant form albeit the inclusion in time variant parameter.
Representation of a lumped model consisting of a voltage source and a resistor. The lumped-element model (also called lumped-parameter model, or lumped-component model) is a simplified representation of a physical system or circuit that assumes all components are concentrated at a single point and their behavior can be described by idealized mathematical models.