Add to ORKGPolynomial systems can be solved via LMI (linear matrix inequality) optimizations by exploiting the SMR (square matricial representation) of polynomials. This paper investigates the worst and best representation matrices obtainable in these LMI optimizations. In particular, it is shown that there always exist representation matrices for which the computation of the sought solutions either cannot be performed or is ill-conditioned. Moreover, it is shown that the best representation matrices for computing the sought solutions can be obtained by adding suitable LMIs, hence preserving the convexity of the optimization. © 2009 by IJAMAS, CESER.link_to_subscribed_fulltex
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Necessary and sufficient conditions are formulated for checking stability of a 2-D polynomial matrix...
In this paper we present a polynomial-time procedure to find a low rank solution for a system of Lin...
Abstract—This paper is concerned with the problem of finding a low-rank solution of an arbitrary spa...
It is known that LMI can be useful for solving systems of polynomial equations and inequalities prov...
This paper considers the problem of solving certain classes of polynomial systems. This is a well kn...
Considers the problem of solving certain classes of polynomial systems. This is a well known problem...
Considers the problem of solving certain classes of polynomial systems. This is a well known problem...
Considers the problem of solving certain classes of polynomial systems. This is a well known problem...
This paper considers the problem of determining the solution set of polynomial systems, a well-known...
Abstract—Numerous tasks in control systems involve opti-mization problems over polynomials, and unfo...
This paper considers the problem of determining the solution set of polynomial systems, a well-known...
This paper considers the problem of determining the solution set of polynomial systems, a well-known...
This paper considers the problem of determining the solution set of polynomial systems, a well-known...
Abstract: Multivariate polynomial system solving and polynomial optimization problems arise as centr...
Necessary and sufficient conditions are formulated for the zeros of an arbitrary polynomial matrix t...
Necessary and sufficient conditions are formulated for checking stability of a 2-D polynomial matrix...
In this paper we present a polynomial-time procedure to find a low rank solution for a system of Lin...
Abstract—This paper is concerned with the problem of finding a low-rank solution of an arbitrary spa...