in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

This paper addresses the problem of designing stabilizing controllers that minimize the 7 l ~ norm of a certain closed-loop transfer function while maintaining the C1 norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in a robust control framework it can be t...

We consider the expected residual minimization formulation of the stochastic R0 matrix linear complementarity problem. We show that the involved matrix being a stochastic R0 matrix is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded. Moreover, local and global error bounds are given for the stochastic R0 matrix li...

We first introduce matrix concepts in linear programming by developing a variation of the simplex method called the revised simplex method. This algorithm, which has become the basis of all commercial computer codes for linear programming, simply recognizes that much of the information calculated by the simplex method at each iteration, as described in Chapter 2, is not needed. Thus, efficienci...

Let D be a non empty set, let us consider k, and let M be a matrix over D. Then M k is a matrix over D. We now state four propositions: (3) For every finite sequence M such that lenM = n+1 holds len(M n+1) = n: (4) Let M be a matrix over D of dimension n+1 m and M1 be a matrix over D. Then (i) if n > 0; then widthM = width(M n+1); and (ii) if M1 = hM(n+1)i; then widthM = widthM1: (5) For every ...