This paper offers necessary and sufficient condition for delay-dependent asymptotic stability of linear discrete systems with multiple time delay. The criterion is derived by Lyapunov’s direct method and two matrix equations have been obtained: discrete Lyapunov matrix equation for nondelay systems and polynomial matrix equation. Obtained stability condition does not possess conservatism but re...

By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton’s method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of ...

Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function φ(Z) = Q − ZPZ′ is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this ...

A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to calculate the strict Chebyshev solution, and (3)...

in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

In this note we report on a new kind of algebraic Ric-cati equation which we encountered when studying an H 1 type problem of disturbance attenuation for stochastic linear systems. The same equation occurs in the analysis of stability radii of linear systems with both deterministic and stochastic uncertainties. The associated linear matrix inequality is also considered.

An iterative algorithm is constructed to solve the linear matrix equation pair AXB E, CXD F over generalized reflexive matrix X. When the matrix equation pair AXB E, CXD F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the ...

The well-known positive real lemma characterizes positive realness of transfer functions of timeinvariant linear systems via the solvability of certain linear matrix inequalities. In this paper, we propose an extension of the positive real lemma and the underlying linear matrix inequalities to descriptor systems. We show that the solvability of these linear matrix inequalities is sufficient and...