A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains...

in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.

This paper presents an elementary solution to the non-singular H" control problem. In this control problem, the underlying linear system satisfies a set of assumptions which ensures that the solution can be obtained by solving just two algebraic Riccati equations of the game type. This leads to the central solution to the H" control problem. The solution presented in this paper uses only elemen...

The problem of robust stability analysis for uncertain discrete singular time-delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncerta...

Abstract: We consider an optimal control problem of the Mayertype for a single-input, control affine, nonlinear system in small dimension. In this paper, we analyze effects that a modeling extension has on the optimality of singular controls when the control is replaced with the output of a first-order, time-invariant linear system driven by a new control. This analysis is motivated by an optim...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

We obtain new conditions sufficient for the (unique, under an additional condition) solvability of a system of singular functional differential equations with non-increasing operators. 1. Problem setting and motivation The aim of this note is to establish some general conditions sufficient for the existence and uniqueness of a slowly growing solution of a class of singular linear functional dif...

We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax = b, we show that this condition number can be computed using the singular values and the right singular vectors of [A, b] and A. We also provide an upper bound that requires the computation of the largest and the smallest singular value of [A, b...