Notes in Week 2 - Intro to other models

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Published	10/15/2024	In the state-space model, the {{c1::state variables}} describe the system's internal condition at any given time.
Published	10/15/2024	The continuous-time state-space equation is typically written as {{c1::\(ẋ(t) = Acx(t) + Bcu(t)\)}}.
Published	10/15/2024	The output equation for a continuous-time state-space model is given by {{c1::\(y(t) = Ccx(t) + Dcu(t)\)}}.
Published	10/15/2024	A {{c1::state-space model}} is used to represent a system in terms of its internal state, inputs, and outputs.
Published	10/15/2024	The state-space model is especially useful for describing systems with multiple {{c1::inputs and outputs}}.
Published	10/15/2024	The discrete-time state-space model is written as {{c1::\(x(t+1) = Ax(t) + Bu(t)\)}}.
Published	10/15/2024	The output equation for the discrete-time state-space model is {{c1::\(y(t) = Cx(t) + Du(t)\)}}.
Published	10/15/2024	Discretizing a continuous-time system is necessary for digital control because {{c1::digital processors}} operate in discrete time.
Published	10/15/2024	{{c1::Matrix exponential}} is used to compute the {{c2::state transition}} matrix in {{c3::continuous-time}} systems.
Published	10/15/2024	The Euler method is a simple numerical approximation used to discretize continuous-time systems, written as {{c1::\(x(t+1) = x(t) + Ts \cdot ẋ(t)\)}}.
Published	10/15/2024	In linear system theory, the {{c1::system matrix (A)}} defines the relationship between the current state and its derivative.
Published	10/15/2024	The {{c1::Input Matrix}} in the state-space model captures how the system's inputs affect its state.
Published	10/15/2024	{{c1::Nonlinear systems}} can often be linearized around an operating point to simplify analysis and control.
Published	10/15/2024	The system matrix {{c1::A}} in discrete-time models can be derived by calculating the {{c1::matrix exponential}}.
Published	10/15/2024	The {{c1::sampling interval (Ts)}} determines the accuracy of a discrete-time model when approximating a continuous-time system.
Published	10/15/2024	In control theory, {{c1::feedback}} is used to regulate the behavior of a system by using its output to influence the input.
Published	10/15/2024	Linear systems are easier to analyze because they follow the principle of {{c1::superposition}}.
Published	10/15/2024	The {{c1::linearization}} of a nonlinear system near an equilibrium point involves approximating the system using its first-order Taylor expansion.
Published	10/15/2024	The {{c1::Jacobian matrix}} is used to linearize nonlinear systems around a specific operating point.
Published	10/15/2024	In a spring-mass system, the state variables represent the {{c1::positions and velocities}} of the masses.
Published	10/15/2024	The {{c1::control input}} in a dynamic system is the external signal applied to influence the system’s behavior.
Published	10/15/2024	In control systems, {{c1::stability}} refers to the ability of a system to return to equilibrium after a disturbance.
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