QUALITATIVE STABILITY CONCEPT FROM ECOLOGY AND ITS USE IN THE ROBUST STABILITY ANALYSIS OF LINEAR INTERVAL PARAMETER SYSTEMS

The paper first reviews the fundamentals related to ‘Qualitative (or Sign) Stability’ of Ecology including the necessary and sufficient conditions for qualitative stability, along with the associated ‘color test'. Then the problem of robust stability analysis of interval parameter matrices is addressed and then using the tool of ‘qualitative stability', a simple sufficient condition for robust stability of a class of interval matrices is obtained. Then the case of matrices in which the interval parameters enter nonlinearly into the entries is considered and again using the qualitative stability of Ecology ideas, sufficient bounds on these parameters are obtained. It is concluded that qualitative stability concept from ecology can be further exploited to solve many other interesting problems in engineering/mathematical sciences.