Dynamic systems with continuous-time models in the form of differential equations possess memory. For systems with memory, knowledge of the system’s inputs at a given point in time is insufficient to determine the state of the system at the same time. For example, a circuit with capacitors and inductors possesses memory. The instantaneous energy stored in the circuit is a function of the current state (capacitor voltages and inductor currents) which depends on the history of its sources (inputs) from the time when the complete state was last known.
An nth-order dynamic system with state variables x1, x2, …, xn and inputs u1, u2, …, um is modeled by expressions for the state derivatives, that ...
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