In this paper we consider the standard linear SDP problem, and its low rank nonlinear programming reformulation, based on a Gramian representation of a positive semidefinite matrix. For this nonconvex quadratic problem with quadratic equality constraints, we give necessary and sufficient conditions of global optimality expressed in terms of the Lagrangian function.

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 ...

In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix f...

Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel’d [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.

The paper addresses the problem to design a quadratic stable output/state feedback model predictive control for linear systems with input constraints. In the proposed design technique the model predictive control is designed for N2 step ahead prediction using the Lyapunov function approach with the cost function guaranteeing input constraints. Output gain matrix calculation is realized off line...

We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinte complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity. We also establish quadratic convergence o...

In this paper we investigate the consistency of parameter estimates obtained from least squares identification with a quadratic parameter constraint. For generality, we consider infinite impulse response systems with colored input and output noise. In the case of finite data, we show that there always exists a possibly indefinite quadratic constraint depending on the noise realization that yiel...

This paper presents necessary and sufficient conditions for quadratic stability and stabilization of uncertain linear discrete systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. The results are obtained in terms of linear matrix inequality. A robustly sta...

This paper deals with the problem of absolute stability of neutral type Lur’e systems with time-varying delays. By constructing new Lyapunov-Krasovskii functional, a matrix-based on quadratic convex approach combining with some improved bounding techniques for integral terms such as Wirtinger-based integral inequality, new stability condition is much less conservative and more general than some...

The transmission matrix, introduced by Friedland in 1957, can be used to characterize a linear, time invariant system having an emprically-determined impulse response. The Wiener-Kalman filter can be determined by Cholesky factorization of a covariance matrix formed from the transmission matrix. An analogous result is given for linear, quadratic control. The method is illustrated by several exa...