Robust Stability and Control of Linear Interval Parameter Systems Using Quantitative (State Space) and Qualitative (Ecological) Perspectives

Abstract

The problem of maintaining the stability of a nominally stable linear time invariant system subject to linear perturbation has been an active topic of research for quite some time. The recent published literature on this `robust stability’ problem can be viewed mainly from two perspectives, namely i) transfer function (input/output) viewpoint and ii) state space viewpoint. In the transfer function approach, the analysis and synthesis is essentially carried out in frequency domain, whereas in the state space approach it is basically carried out in time domain. Another perspective that is especially germane to this viewpoint is that the frequency domain treatment involves the extensive use of `polynomial’ theory while that of time domain involves the use of ‘matrix’ theory. Recent advances in this field are surveyed in [1]-[2]. Even though in typical control problems, these two theories are intimately related and qualitatively similar, it is also important to keep in mind that there are noteworthy differences between these two approaches (‘polynomial’ vs ‘matrix’) and this chapter (both in parts I and II) highlights the use of the direct matrix approach in the solution to the robust stability and control design problems.