ABSTRACT
The stability of a system is that property of the system which determines whether its response to inputs, disturbances, or initial conditions will decay to zero, is bounded for all time, or grows without bound with time. This chapter presents stability and relative stability for linear time-invariant systems and both continuous-time and discrete-time. Absolute stability is a binary condition: either a system is stable or it is unstable, never both. The chapter discusses several mathematical models for linear time-invariant systems. The Routh test provides information pertaining to stability and the number of unstable poles of a system. The Jury test for determining the stability of discrete-time systems is similar to the Routh criterion for continuous-time systems and is much simpler to implement than the Schur-Cohn test. Where the Routh test determines if the roots of a polynomial equation are in the left half plane, the Jury test determines whether the roots of a polynomial equation are inside the unit circle.
