Stability analysis using GUI in MATLAB (Electronic Engineering) Project Proposal - Essay Example

Initially it is essential to examine the theoretical basis for the concept of stability in order to identify the various conditions which characterize a stable system. After determining the stability conditions, the Graphical User Interface Development Environment (GUIDE) module of MATLAB will be studied to examine the process of developing a Graphical User Interface for a MATLAB application which determines the stability of a given system. The BIBO (Bounded Input Bounded Output) concept of stability states that if a bounded input to the system produces a bounded output, then the system is stable (Ogata. K. 1997).

It is important to determine the physical significance of stability both in the time domain and in the frequency domain. In the time domain, for continuous functions to be BIBO stable, an integral of their impulse response should exist. Similarly for discrete functions in the time domain, we should be able to sum up the impulse responses of the discrete function (Ogata. K. 1995). To determine stability in the frequency domain, we consider the Laplace transform (used for converting continous functions from time domain to frequency domain and vice versa) for the continous signals and Z transform (used for converting discrete functions from time domain to frequency domain and vice versa) for the discrete signals.

If the region of convergence of the Laplace transform includes the imaginary axis, then the system is stable (Ogata. K. 1995). The physical significance of this statement is that all poles of the system should on the left of the origin (as we are dealing only with causal systems). If the region of convergence Z transform includes the unit circle then the system is stable. A system is stable if and only if all its poles are lying within the unit circle. The transfer function is an illustration of the relationship between the input to a system and the output of the system (Ogata. K. 1997).

It accurately represents a system which is time invariant