A state-space model is commonly used for representing a linear time-invariant (LTI) system. It describes a system with a set of first-order differential or difference equations using inputs, outputs, and state variables. In the absence of these equations, a model of a desired order (or number of states) can be estimated from measured input-output data.
The models are widely used in modern control applications for designing controllers and analyzing system performance in the time domain and frequency domain. The models can be applied to nonlinear systems or systems with non-zero initial conditions. They also provide a convenient way to represent, analyze, and control multi-input/multi-output (MIMO) systems.