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In control theory, the state-transition matrix is a matrix whose product with the state vector at an initial time gives at a later time . The state-transition matrix can be used to obtain the general solution of linear dynamical systems.
This state-space realization is called controllable canonical form (also known as phase variable canonical form) because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state).
In control theory, we may need to find out whether or not a system such as ... is the state transition matrix of ˙ = (), is ...
Control theory [ edit ] The fundamental matrix is used to express the state-transition matrix , an essential component in the solution of a system of linear ordinary differential equations.
In the state-transition table, all possible inputs to the finite-state machine are enumerated across the columns of the table, while all possible states are enumerated across the rows. If the machine is in the state S 1 (the first row) and receives an input of 1 (second column), the machine will stay in the state S 1.
The exact definition varies slightly within the framework or the type of models applied. The following are examples of variations of controllability notions which have been introduced in the systems and control literature: State controllability; Output controllability; Controllability in the behavioural framework
In the discrete-time case with uncertainty about the parameter values in the transition matrix (giving the effect of current values of the state variables on their own evolution) and/or the control response matrix of the state equation, but still with a linear state equation and quadratic objective function, a Riccati equation can still be ...
In control engineering and system identification, a state-space representation is a mathematical model of a physical system specified as a set of input, output, and variables related by first-order differential equations or difference equations.