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This paper gives a necessary and sufficient condition for the Hurwitz stability of interval matrices [formulas], where [formula] are symmetrizable by the matrix [formula]. This result is a generalization of the papers [3], [4], where it was assumed that the matrices [formula] are symmetric.
The systems under consideration are governed by a set of first-order linear partial differential hyperbolic equations together with boundary conditions. The Lyapunov method is used to verify the stability of the initial-boundary value problem. Necessary and sufficient conditions for stability are obtained under the assumption that the matrix coefficients in the differential equations and in the boundary...
An LMI approach to investigating the stability and related problems for linear three-dimensional discrete systems is described. The stability and lower bounds for stability margins are discussed for all principal three-dimensional state-space models. The particular emphasis is put on the robust stability for the uncertain case. A numerical example is presented to illustrate the results developed in...
Necessary and sufficient conditions for robust stability of the positive discrete-time interval system with time-delays are established. It is shown that this system is robustly stable if and only if one well defined positive discrete-time system with time-delays is asymptotically stable. The considerations are illustrated by numerical example.
Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems wit h delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed condi-tions are compared wit h the suitable conditions for the standard systems. The considerations are illustrated by numerical...
Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system without delays of the same size. The considerations are illustrated by numerical examples.
In this paper, a system of Lyapunov equations A*i P + PAi = −Qi (i = 1, . . . ,m), (A) is considered in which Ai are given n × n complex matrices, Qi are unknown n × n Hermitian positive definite matrices and P, if any, is a common solution to the Lyapunov equations (A). Both sufficient and necessary and sufficient conditions are derived for the existence of such a matrix P. Examples are presented...
By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.
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