摘要：The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these *** solutions have been proposed,most of which are based on finding the existence of a common Lyapunov function(CLF) or a multiple Lyapunov function(MLF) where the key is to formulate the problem into a set of linear matrix inequalities(LMIs).An alternative method for finding the existence of a CLF by solving two sets of linear inequalities(LIs) has previously been *** method is seen to be less computationally taxing compared to methods based on solving *** substantiate this,the computational ability of three numerical computational solvers,LMI solver,cvx,and Yalmip,as well as the symbolic computational program Maple were tested.A specific switched system comprising four second-order subsystems was used as a test *** the obtained solutions,the validity of the controllers and the corresponding CLF was *** was found that all tested solvers were able to correctly solve the *** issue of rounding-off error in numerical computation based software is discussed in *** test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal *** use of different external solvers led to the same conclusion in terms of the stability of switched *** a result,a shift from using a conventional numerical computation based program to using computer algebra is suggested.

摘要：3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A method for normalizing moments of 3D objects is proposed, which can set the values of moments of different orders roughly in the same range and be applied to different 3D data formats universally. Then accurate computation of moments for several objects is presented and experiments show that this kind of normalization is very useful for moment invariants in 3D objects analysis and recognition.