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This paper introduces a positive real lemma for continuous-time singular hybrid systems. The necessary and sufficient condition of stochastic admissibility and strict passivity for the singular hybrid systems is obtained in terms of linear matrix inequalities. The sufficient condition is derived by using mode-dependent Lyapunov function. In this step, two slack variables are inserted to make the proposed condition be necessary and sufficient condition in terms of strict linear matrix inequalities. Then, to prove the necessary condition, the positive real lemma for the hybrid system is proposed. Since the admissible singular system can be reformulated into stable normal system, the positive real lemma for the hybrid system holds. Thus, we give a necessary condition by constructing the solution of the proposed lemma from that of the hybrid systems.

This paper presents a dynamic output-feedback stabilization problem of descriptor Markovian jump systems with generally uncertain transition rates. First, a new necessary and sufficient condition to relax inequalities including generally uncertain transition rates is introduced. For the closed-loop systems with a dynamic output-feedback controller, the stabilization criterion is achieved as non-convex matrix inequalities. For the obtained criterion, this paper gives an improved necessary and sufficient condition in terms of linear matrix inequalities under completely known transition rates. Then, the proposed condition is extended for the descriptor Markovian jump systems with generally uncertain transition rates. To show the validity of the proposed control, a numerical example is given.

The mechanical, thermal, and morphological behavior of poly(ethylene terephthalate)/high density polyethylene (PET/HDPE) blends with/without poly(ethylene-co-acrylic acid) (PEAA) as a reactive compatibilizer were investigated. The addition of PEAA improves the mechanical properties such as flexural yield strain and impact strength when HDPE forms matrix phase. On the other hand, when the PET is the matrix, no significant improvement of mechanical properties is observed, suggesting that the crystallization rate can be an important factor in the blend composed of two crystalline components. The addition of PEAA also affects morphological features such as reducing the size of the dispersed phase and making the interface obscure indicating the role of PEAA as a reactive compatibilizer. The crystallinity of PET and HDPE is slightly reduced by the addition of PEAA. The content of acrylic acid (AA) in PEAA also has an effect on mechanical properties and morphology, suggesting the added PEAA goes to the HDPE phase as well as the interface between PET and HDPE.