A characterization of convex cones of matrices with constant regular inertia

AbstractLet A be a convex cone of n×n matrices. In this paper, we present a necessary and sufficient condition for A to contain matrices with a constant regular inertia, based on a version of the Lyapunov equation. The condition involves only the normalized extreme points of A. This extends a previous paper by the authors, where a robust stability criterion for A was obtained

On Stability of Parametrized Families of Polynomials and Matrices

The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices is equivalent to the nonsingularity of the family {2−2+∶∈,∈[−1,1]} if has at least one stable member. Based on the Bernstein expansion of a multivariable polynomial and extremal properties of a multilinear function, fast algorithms are suggested

Robust unknown input observer for state and fault estimation in discrete-time Takagi-Sugeno systems

In this paper, a robust unknown input observer (UIO) for the joint state and fault estimation in discrete-time Takagi-Sugeno (TS) systems is presented. The proposed robust UIO, by applying the H-infinity framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy.Postprint (author's final draft

A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems

This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi-Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi-Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi-Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the teachability analysis can be performed efficiently using the proposed approach.This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi-Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi-Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi-Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the teachability analysis can be performed efficiently using the proposed approach.Postprint (author's final draft

Convex combinations of matrices - nonsingularity and schur stability characterizations

Elsner L, Szulc T. Convex combinations of matrices - nonsingularity and schur stability characterizations. Linear and Multilinear Algebra. 1998;44(4):301-312