Quadratic Matrix Inequalities and Stability of Polynomials
نویسنده
چکیده
New relationships are enlightened between various quadratic matrix inequality conditions for stability of a scalar polynomial. It is namely shown how a recently published linear matrix inequality condition can be derived from Hermite and Lya-punov stability criteria.
منابع مشابه
Complete quadratic Lyapunov functionals for distributed delay systems
This paper is concerned with the stability analysis of distributed delay systems using complete-Lyapunov functionals. Numerous articles aim at approximating their parameters thanks to a discretization method or polynomial modeling. The interest of such approximations is the design of tractable sufficient stability conditions. In the present article, we provide an alternative method based on pol...
متن کاملQuadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|
متن کاملThe Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials
In this paper, we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays. Constant or pantograph delays may appear in state-control or both. We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then, these are utilized to reduce the solution of optimal control with constant...
متن کاملRobust Stability of Polytopic Systems via Homogeneous Polynomials
This paper considers the robust stability problem for state space models via homogeneous polynomially parameter-dependent Lyapunov functions. The suggested approach is based on a quadratic in the vector of parametric monomials matrix representation of the time derivative of the Lyapunov function. At each step, sufficiency is provided by a set of relaxed linear matrix inequalities and check for ...
متن کاملA convex optimisation approach to robust observer-based H∞ control design of linear parameter-varying delayed systems
Abstract: This paper presents a convex optimisation method for observer-based control design of LPV neutral systems. Utilising the polynomials parameter-dependent quadratic functions and a suitable change of variables, the required sufficient conditions with high precision for the design of a desired observer-based control are established in terms of delay-dependent parameter-independent linear...
متن کامل