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Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal. When a discrete-time signal is obtained by sampling a sequence at uniformly spaced times, it has an associated sampling rate. Discrete-time signals may have several ...
Continuous dynamic systems (like physical systems with material objects moving in space) are characterized by state variables the values of which change continuously, while the state variable values of discrete dynamic systems (like predator-prey ecosystems) "jump", that is, they are changed at discrete time steps only. In continuous simulation ...
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati equation is similar to one of the following: the continuous time algebraic Riccati equation (CARE): + + = or the discrete time algebraic Riccati ...
Unlike traditional numerical solution methods, which approach the problem by discretizing time and solving for the next (real-valued) state at each successive time step, QSS methods keep time as a continuous entity and instead quantize the system's state, instead solving for the time at which the state deviates from its quantized value by a ...
The equation is named after Jacopo Riccati (1676–1754). [1] More generally, the term Riccati equation is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control.
The systems are typically described by ordinary differential equations or partial differential equations. A simulation run solves the state-equation system to find the behavior of the state variables over a specified period of time. The equation is solved through numerical integration methods to produce the transient behavior of the state ...
In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is A X A H − X + Q = 0 {\displaystyle AXA^{H}-X+Q=0} where Q {\displaystyle Q} is a Hermitian matrix and A H {\displaystyle A^{H}} is the conjugate transpose of A {\displaystyle A} , while the continuous-time Lyapunov equation is
A solution to a discretized partial differential equation, obtained with the finite element method. In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...