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Additive State Decomposition
Additive state decomposition occurs when a system is decomposed into two or more subsystems with the same dimension as that of the original system. A commonly used decomposition in the control field is to decompose a system into two or more lower-order subsystems, called lower-order subsystem decomposition here. In contrast, additive state decomposition is to decompose a system into two or more subsystems with the same dimension as that of the original system. Taking a system for example, it is decomposed into two subsystems: and , where and , respectively. The lower-order subsystem decomposition satisfies : n = n_p + n_s\text P = P_p \oplus P_s By contrast, the additive state decomposition satisfies : n = n_p = n_s \text P = P_p + P_s On a dynamical control system Consider an 'original' system as follows: where x\in\R^n. First, a 'primary' system is brought in, having the same dimension as the original system: where x_p\in\R^n. From the original system and the primary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek language, Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα" Henry George Liddell, Robert Scott, ''A Greek–English Lexicon'', on Per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subsystem
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα" Henry George Liddell, Robert Scott, '' |
Dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A Surface (mathematics), surface, such as the Boundary (mathematics), boundary of a Cylinder (geometry), cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the Euclidean plane, plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive State Decomposition On A Dynamical Control System
Additive may refer to: Mathematics * Additive function, a function in number theory * Additive map, a function that preserves the addition operation * Additive set-functionn see Sigma additivity * Additive category, a preadditive category with finite biproducts * Additive inverse, an arithmetic concept Science * Additive color, as opposed to subtractive color * Additive model, a statistical regression model * Additive synthesis, an audio synthesis technique * Additive genetic effects * Additive quantity, a physical quantity that is additive for subsystems; see Intensive and extensive properties Engineering * Feed additive * Gasoline additive, a substance used to improve the performance of a fuel, lower emissions or clean the engine * Oil additive, a substance used to improve the performance of a lubricant * Weakly additive, the quality of preferences in some logistics problems * Polymer additive * Pit additive, a material aiming to reduce fecal sludge build-up and control od ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Principle
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input ''A'' produces response ''X'' and input ''B'' produces response ''Y'' then input (''A'' + ''B'') produces response (''X'' + ''Y''). A function F(x) that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: additivity F(x_1+x_2)=F(x_1)+F(x_2) \, and homogeneity F(a x)=a F(x) \, for scalar . This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
