ABSTRACT
This chapter introduces the algebraic methods to analyze state variable models of dynamic systems. It describes the models in terms of first-order ordinary differential equations (ODEs) involving time derivatives of a set of state variables, that is, the natural variables associated with the energy storage elements or alternate variables used to describe the system. The chapter focuses on the single-input single-output systems that are described by a rational transfer function. However, the methods presented can be easily generalized to include multi-input multi-output systems. The chapter describes the analysis techniques for state variable models of the continuous-time systems. These techniques are later extended to state variables models of sampled-data systems. The state equations of a system comprise first-order ODEs that describe dynamic system behavior in terms of time derivatives of a set of state variables. The chapter discusses the problem of realizing a transfer function model as a state variable model.
