in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

The paper investigates delay-dependent control and stability analysis for T−S fuzzy systems with a sensor delay. Based on a Lyapunov-Krasovskii function (LKF), a less conservative delay-dependent stability condition in the form of parameterized linear matrix inequalities (PLMIs) is established. In the derivation process, Jensen inequality is introduced to estimate the upper bound of the derivat...

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set methods that solve only one linear system of equations per iteration. The linear solver, preconditioner, and matrix structures can be chosen by the user for a pa...

This paper presents stability analysis and robust H∞ control for nonlinear switched systems bounded in sectors with arbitrary boundaries. By proposing new and more general multiple Lyapunov functions that incorporate nonlinearities in the system, we formulate the stability conditions under arbitrary switching in the form of linear matrix inequalities. Moreover, an optimization problem subject t...

Abstract: The purpose of the paper is to present a class of algorithms using to solve the optimization problem concerning with H∞ feedback control for linear discrete-time stochastic systems with stochastic parameter uncertainties, as well as a method for the optimization problem reducing this to a standard formulation used two convex inequalities, which can be solved by linear matrix inequalit...

A procedure for identifying a linear MIMO model with LFT-type uncertainty is presented. The uncertainty is minimized subject to the requirement that known input-output data do not invalidate the model. The optimization problem is solved stepwise. First, the uncertainty is minimized frequency-byfrequency with respect to the sampled frequency response of a nominal model subject to data-matching c...

In this paper is analyzed the minimal correction problem for an inconsistent linear inequality system. By the correction we mean avoiding its contradictory nature by means of relaxing the constraints. When the system of inequalities Ax ≤ b has no solutions, we are interested in a vector that satisfies the system in a Least Squares (LS) sense, i.e. a vector x ∈ R that minimizes the quantity ∥∥(A...

The wide applicability of chance–constrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so–called safe tractable approximations of chance–constrained programs, where a chance constraint is replaced by a...

abstract. the main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. properties of the legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. afterwards, an iterative algorithm is examined for solvin...