System identification is the process of constructing a mathematical model from input and output data for a system under testing, and characterizing the system uncertainties and measurement noises. The mathematical model structure can take various forms depending upon the intended use. The SYSTEM/OBSERVER/CONTROLLER IDENTIFICATION TOOLBOX (SOCIT) is a collection of functions, written in MATLAB language and expressed in M-files, that implements a variety of modern system identification techniques.

For an open-loop system, the central features of the SOCIT are functions for identification of a system model and its corresponding forward and backward observers directly from input and output data. The system and its observers are represented by a discrete model. The identified model and observers may be used for controller design of linear systems as well as identification of modal parameters such as damping, frequency, and mode shape. For a closed-loop system, the central features of the SOCIT include identification of an open-loop model, an observer and its corresponding controller gain directly from input and output data.

The basic package is capable of:

• Identifying system, forward and backward observer Markov parameters (pulse responses) from input and output time histories.
  
• Constructing a state space model from pulse responses.
  
• Identifying a state space model and its corresponding forward and backward observer gains directly from input and output time histories.
  
• Identifying a forward observer/Kalman filter gain with a given state space model, and input and output time histories.
  
• Computing variance and bias for identified modal parameters using Monte Carlo and perturbation procedures.
  
• Computing forward prediction errors and backward smoothing errors for any of the models generated. 
  
• Identifying a state space model, and its corresponding controller gain and observer/Kalman filter gain directly from input, output and control force time histories.