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- State-Transition_Equation abstract "The State-transition equation is defined as the solution of the linear homogeneous state equation. The linear time-invariant state equation is given bycan be solved by using either the classical method of solving linear differential equations or the Laplace transform method. The Laplace transform solution is presented in the following equations.Laplace transform of the above equation yields where x(0) denotes Initial-state vector evaluated at . Solving for So, the state-transition equation can be obtained by taking inverse Laplace transform as The state-transition equation as derived above is useful only when the initial time is defined to be at . In the study of control system, specially discrete-data control system, it is often desirable to break up a state-transition process into a sequence of transitions, so a more flexible initial time must be chosen. Let the initial time be represented by and the corresponding initial state by , and assume that the input and the disturbance are applied at t≥0. We start with the above equation by setting and solving for , we get Once the state-transition equation is determined, the output vector can be expressed as a function of initial state.".
- State-Transition_Equation wikiPageExternalLink node411.html.
- State-Transition_Equation wikiPageExternalLink StateSpaceResponse.pdf.
- State-Transition_Equation wikiPageExternalLink control.
- State-Transition_Equation wikiPageExternalLink State-Space_Equations.
- State-Transition_Equation wikiPageID "41555646".
- State-Transition_Equation wikiPageRevisionID "589389403".
- State-Transition_Equation subject Category:Control_theory.
- State-Transition_Equation comment "The State-transition equation is defined as the solution of the linear homogeneous state equation. The linear time-invariant state equation is given bycan be solved by using either the classical method of solving linear differential equations or the Laplace transform method. The Laplace transform solution is presented in the following equations.Laplace transform of the above equation yields where x(0) denotes Initial-state vector evaluated at .".
- State-Transition_Equation label "State-Transition Equation".
- State-Transition_Equation sameAs m.0_1dc4m.
- State-Transition_Equation sameAs Q17014424.
- State-Transition_Equation sameAs Q17014424.
- State-Transition_Equation wasDerivedFrom State-Transition_Equation?oldid=589389403.
- State-Transition_Equation isPrimaryTopicOf State-Transition_Equation.