The function does not depend explicitly on time, i.e. There are two common simplifications which make the problem more tractable. The relationship given in Equation (1) is very general and can be used to describe a wide variety of different systems unfortunately, The system order usually corresponds to the number of independent energy storage elements in the system. is referred to as the system order and determines the dimensionality of the state-space. , required in order to capture the "state" of a given system and to be able to predict the system's future behavior (solve Though the state variables themselves are not unique, there is a minimum number of state variables, The state at any future time,, may be determined exactly given knowledge of the initial state,, and the time history of the inputs,, between and by integrating Equation (1). is the vector of external inputs to the system at time, and is a (possibly nonlinear) function producing the time derivative (rate of change) of the state vector,, for a particular instant of time.
For instance, in a simple mechanical mass-spring-damper system, the two state variables could be the position and velocity In the above equation, is the state vector, a set of variables representing the configuration of the system at time. For many physical systems, this rule can be stated asĪ set of first-order differential equations: Entering Transfer Function Models into MATLABÄynamic systems are systems that change or evolve in time according to a fixed rule.Entering State-Space Models into MATLAB.