A new method for designing a minimal order perfect functional observers for singular continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of the minimal order perfect functional observer are established. A procedure for computation of matrices of the observers is derived and illustrated by a numerical example. Key-Words: Design, existence, minimal or...

According to conventional wisdom, linear thinking describes thought process that is logical or step-by-step (i.e. each step must be completed before the next one is undertaken). Nonlinear thinking, on the other hand, is the opposite of linear: creative, original, capable of leaps of inference, etc. From a complexity-theoretic viewpoint, conventional wisdom turns out to be startlingly right in t...

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

In this article a detailed overview of Lyapunov stability of linear continuous systems is presented. The conditions for the existence of the solutions for both regular and irregular singular linear systems are introduced. To guarantee an asymptotical stability for linear continuous singular systems and to provide an impulse-free motion of the system, new stability conditions are analyzed. In th...

In this paper, we introduce the notion of geometric Riemann scheme of the sixth Painlevé equation, which consists of the pair of accessible singular points and matrix of linear approximation around each singular point on the boundary divisor in the Hirzebruch surface. Giving this in the differential system satisfying certain conditions, we can recover the Painlevé VI system with the polynomial ...