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The problem of delay-dependent robust H∞ control for uncertain singular systems with multiple state delays has been studied. Firstly, using linear matrix inequality (LMI) approach, an improved delay-dependent criterion is given to ensure the singular system to be regular, impulse free and stable with H∞ performance. Based on this criterion, the problem is solved via state feedback controller, which guarantees that the closed-loop system is not only regular, impulse free and stable, but also satisfying a prescribed H∞ performance condition for all admissible uncertainties. Finally, numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A mixed optimal model approximation is presented to obtain reduced-order models for truly fast descriptor systems. By a projection from truly fast descriptor systems to discrete-time systems, a mixed optimal model approximation for truly fast descriptor systems is transformed to a mixed optimal model approximation of the corresponding discrete-time systems. The structure of the fast descriptor systems is preserved in the model approximation procedure. The expression of the error and its gradient are given explicitly in terms of the solutions of certain Lyapunov equations. A numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We numerically study the thermodynamic properties of two Archimedean lattices1 with Ising spins using Wang–Landau algorithm of the Monte Carlo simulation. The two Archimedean lattices are of the type (3, 122) and Kagomé, for which we are particularly interested in the frustration effects. The internal energy, specific heat, free energy, entropy, magnetization and spin susceptibility are calculated. [ABSTRACT FROM AUTHOR]