ABSTRACT
Most of the material covered in the text up to now deal with the complex variable
transform description of dynamic systems without any emphasis on the system
structure or any regard to the system synthesis or design. In this chapter, the state
variable description of the system is presented, which helps us look at the internal
structure of the system along with the input-output system performance. The State
Variable representation highlights the role played by energy storage elements such
as capacitors, reactors, springs and masses, etc. Instead of just the input-output
model, we are able to examine the effect of various driving inputs on the different
internal components and their performance (controllability concept) and the influ-
ence of the different sensing and measuring components on the outputs (observabil-
ity concept). In general, the state space description yields much more information
about the system than the transfer function and often leads to methodical synthesis
and design algorithms. The state variable single order differential equation model
Besides
concise and compact notation, the well-developed apparatus of linear vector spaces
and matrix algebra yields rich dividends. In what follows we present methods for
deriving state space equations and methods for solving them using matrix algebra.
The state of a dynamical system at some time t = t0 is defined by any complete
independent set of system variables whose values at t = t0, along with the knowl-
edge of input functions for t ≥ t0, completely determines the future system behavior. In general, the variables associated with each of the energy storage elements can be
taken as state variables.
