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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 alternative terminology uses continuous parameter as being more inclusive. [1] A more restricted class of processes are the continuous stochastic processes; here the term often (but not always [2]) implies both that the index variable is continuous and that sample paths of the process are continuous. Given the possible confusion, caution is ...
Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next.
For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems. Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i.e. the real part of each pole must be less than zero. Practically speaking, stability requires ...
The examples thus far have shown continuous time systems and control solutions. In fact, as optimal control solutions are now often implemented digitally , contemporary control theory is now primarily concerned with discrete time systems and solutions.
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to ...
The definition for discrete-time systems is almost identical to that for continuous-time systems. The definition below provides this, using an alternate language commonly used in more mathematical texts. Let (X, d) be a metric space and f : X → X a continuous function.
Block diagram illustrating the superposition principle and time invariance for a deterministic continuous-time single-input single-output system. The system satisfies the superposition principle and is time-invariant if and only if y 3 (t) = a 1 y 1 (t – t 0) + a 2 y 2 (t – t 0) for all time t, for all real constants a 1, a 2, t 0 and for all inputs x 1 (t), x 2 (t). [1]