State-space representation

In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.

To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. The state-space method is characterized by significant algebraization of general system theory, which makes possible to use Kronecker vector-matrix structures. The capacity of these structures can be efficiently applied to research systems with modulation or without it. The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With $p$ inputs and $q$ outputs, we would otherwise have to write down $q \times p$ Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions.

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State

State may refer to:

Law and politics

State (polity), an organized political community living under a single system of government

Sovereign state, a sovereign political entity in international law, commonly referred to as a "country"

The Estates or the States, a national assembly of the estates, a legislature

Rechtsstaat, the legal state (constitutional state, state subordinated to law) in philosophy of law and as principle of many national constitutions

Constituent state, a type of political subdivision of a nation

Federated state, a constituent state that is part of a federal model and shares sovereignty with the federal government
U.S. state, a constituent state of the United States, the most prominent example of a federated constituent state

Federated state, a constituent state that is part of a federal model and shares sovereignty with the federal government

U.S. state, a constituent state of the United States, the most prominent example of a federated constituent state

Science and technology

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State (magazine)

State.ie (formerly State Magazine) is an Irish website and formerly a monthly music magazine, which launched in April 2008 and ceased to print in January 2009 having published a total of ten issues. The magazine continues online and was voted Best Music Site in 2008 and Best Web Publication in 2010 in the Irish Web Awards. Originally the concept of the magazine involved a hard copy of which there was a charge to purchase, however after six issues it was decided to make the magazine's content free both online and in print. The first issue, April 2008, appeared on Irish shelves on 6 March 2008 and featured Michael Stipe of R.E.M. on the cover. This immediately garnered comparisons between the new magazine's similarities with Hot Press who featured Stipe on their cover at the same time, a move widely thought to be an attempt by Hot Press to stifle State's status as a serious 'alternative' to the more established local magazine. At a price of €5.50, State charged €2 more than Hot Press.

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State (CTA Englewood Line station)

State was a station on the Englewood Branch of the Chicago 'L'. The station opened on November 3, 1905 and closed on September 2, 1973 as part of a group of budget-related CTA station closings.