The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
This paper presents a new noise immunity encoding/decoding technique by using the features of triple correlation and bispectrum widely employed in digital signal processing systems operating in noise environments. The triple correlationand bispectrum-based encoding/decoding algorithm is tested for a digital radio telecommunications binary frequency shift keying system. The errorless decoding probability was analyzed by means of computer simulation for the transmission and reception of a test message...
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...
A synthesis of recent development of regime-switching models based on aggregation operators is presented. It comprises procedures for model specification and identification, parameter estimation and model adequacy testing. Constructions of models for real life data from hydrology and finance are presented.
We consider the one dimensional semilinear reaction-diffusion equation, governed in Ω = (0,1) by controls, supported on any subinterval of (0, 1), which are the functions of time only. Using an asymptotic approach that we have previously introduced in [9], we show that such a system is approximately controllable at any time in both L2(0,1)( and C0[0,1], provided the nonlinear term f = f(x,t, u) grows at infinity no faster than certain power of log |u|. The latter depends on the regularity...
In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.
In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.
We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular,...
We analyze the controllability of the motion of a fluid by means of the action of a vibrating shell coupled at the boundary of the fluid. The model considered is linear. We study its approximate controllability, i.e. whether the fluid may reach a dense set of final configurations at a given time. We show that this problem can be reduced to a unique continuation question for the Stokes system. We prove that this unique continuation property holds generically among analytic domains and therefore,...