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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 {\displaystyle p} inputs and q {\displaystyle q} outputs, we would otherwise have to write down q × p {\displaystyle q\times p} Laplace transforms to encode all ...
Vacuum World, a shortest path problem with a finite state space. In computer science, a state space is a discrete space representing the set of all possible configurations of a "system". [1] It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .
Consider a physical system modeled in state-space representation.A system is said to be observable if, for every possible evolution of state and control vectors, the current state can be estimated using only the information from outputs (physically, this generally corresponds to information obtained by sensors).
For the simplest example of a continuous, LTI system, the row dimension of the state space expression ˙ = + determines the interval; each row contributes a vector in the state space of the system. If there are not enough such vectors to span the state space of x {\displaystyle \mathbf {x} } , then the system cannot achieve controllability.
Kálmán published several seminal papers during the sixties, which rigorously established what is now known as the state-space representation of dynamical systems. He introduced the formal definition of a system, the notions of controllability and observability, eventually leading to the Kalman decomposition.
In systems and control theory, the double integrator is a canonical example of a second-order control system. [1] ... and the state space representation:
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 the desired property. Problems are often modelled as a state space, a set of states that a problem