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 or difference equations. State variables are variables whose values evolve through time in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables. The "state space" is the Euclidean space in which the variables on the axes are the state variables. The state of the system...

In physics, a state space is an abstract space in which different "positions" represent, not literal locations, but rather states of some physical system. This makes it a type of phase space. Specifically, in quantum mechanics a state space is a complex Hilbert space in which the possible instantaneous states of the system may be described by unit vectors. These state vectors, using Dirac's bra–ket notation, can often be treated like coordinate vectors and operated on using the rules of linear algebra. This Dirac formalism of quantum mechanics can replace calculation of complicated integrals with...

State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with a desired property. Problems are often modelled as a state space, a set of states that a problem can be in. The set of states forms a graph where two states are connected if there is an operation that can be performed to transform the first state into the second. State space search often differs from traditional computer science search methods because the state space...