ABSTRACT
In this chapter, we describe the important attributes of simple, linear, time-invariant (LTI) systems. e art of solving the ordinary dierential equations (ODEs) that describe the input and output behavior of continuous, LTI systems is introduced. Matrix algebra and matrix operations are reviewed in Section 2.3, and the state variable (SV) formalism for describing the behavior of high-order, continuous dynamic systems is described in Section 2.3.4. Section 2.4 treats the mathematical tools used to characterize LTI systems and the concepts of system impulse response, real convolution, transient response, and steady-state sinusoidal (SSS) frequency response, including Bode and Nyquist plots, are introduced. Section 2.5 treats discrete LTI (numerical) systems. Dierence equations replace ODEs in describing system behavior in the time domain and use of the z-transform is introduced as a means of solving discrete-state equations. Finally, in Section 2.5, we consider factors aecting the stability of LTI systems.
