Pseudospectra associated with the standard and generalized eigenvalue problems have been widely investigated in recent years. We extend the usual definitions in two respects, by treating the polynomial eigenvalue problem and by allowing structured perturbations of a type arising in control theory. We explore connections between structured pseudospectra, structured backward errors, and structure...

In this paper, optimal control for stochastic linear singular Takagi-Sugeno (T-S) fuzzy system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using ACP approach. The solution of this novel method is compared with the ...

In this paper, we first give the maximal and minimal values of the ranks and inertias of the quadratic matrix functions q1(X) = Q1 − XP1X and q2(X) = Q2 − XP2X subject to a consistent matrix equation AX = B, where Q1, Q2, P1 and P2 are Hermitian matrices. As applications, we derive necessary and sufficient conditions for the solution of AX = B to satisfy the quadratic equality XP1X ∗ = Q1 and X...

In this paper Kharitonov's theorem for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. I t is shown that if the four Hermite matrices corresponding to the four Kharitonov extreme polynomials are positive definite, the Hermit...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...