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The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
State/Space theory constitutes a new branch of social and political geography in which the issues of space as a geographic element are considered for their influence on political relationships and outcomes. [1] Leading scholars include Neil Brenner at the Harvard Graduate School of Design, and Bob Jessop at Lancaster University in England ...
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In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to ...
In 1897, the geographer and ethnographer Friedrich Ratzel in his book Politische Geographie applied the word Lebensraum ("living space") [2] to describe physical geography as a factor that influences human activities in developing into a society. [12] In 1901, Ratzel extended his thesis in his essay titled "Lebensraum ". [13]
The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness, [1] prompting research to improve them. This was the start of the theory of robust control, which took shape in the 1980s and 1990s and is still active today.
In discrete-time the transfer function is given in terms of the state-space parameters by + = and it is holomorphic in a disc centered at the origin. [4] In case 1/ z belongs to the resolvent set of A (which is the case on a possibly smaller disc centered at the origin) the transfer function equals D + C z ( I − z A ) − 1 B {\displaystyle D ...
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems (especially partial differential equations).They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems.