Control of Singular Systems with Random Abrupt Changes
Singular systems also referred to as descriptor systems, implicit systems, gener- ized state-space systems, di?erential-algebraic systems or semi-state systems (see [43, 76]) represents an interesting class of dynamical systems since it combines d- ferential equations and algebraic equations and generalizes the linear time invariant model which is extensively used in linear control theory. This class of systems has been used to model varieties of systems like economics, chemical processes, - chanics, electrical systems, etc. Singular systems have attracted a lot of researchers from the mathematical and control communities and a great number of fundam- tal notions and results in control and systems theory based on linear time-invariant systems with state space representation have been successfully extended to the class of singular systems. For more details on what it has been done on this subject we refer the reader to [3, 4, 51, 75, 122, 123, 127, 50, 109, 112, 122, 124, 126], and the references therein. More speci?cally, we tackled the stability and the stabilizability of the class of linear continuous-time singular systems and many results have been reported in the literature in the LMI setting. Among these results we quote those of . The robust stability and the robust stabilization have also been studied. Many typesof uncertaintieshavebeen consideredamongthem we quotethe normbounded form,the linear fractionaltransformation(LFT, which generalizesthe norm bounded type) and polytopic form. TheH controland the ?ltering problemshave also been treated and interesting ? results werereportedintheliterature.
First book about control of stochastic singular systemsPresents the necessary mathematical and design tools for singular systems