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Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional

Stojanovic S. B., Debeljkovic D. Lj., Antic D. S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 2

479--487

In this paper, the problems of finite-time stability and stabilization for a class of singular time-delay systems are studied. Using the Lyapunov-like functional (LLF) with (exponential or power) weighting function and a new estimation method for the lower bound on LLF, some sufficient stability conditions are introduced. It is shown that the weighting function significantly reduces the conservatism of the stability criteria in comparison to estimation of the lower bound on LLF without this function. To solve the finite-time stabilization problem, a stabilizing linear state controller is designed by exploiting the cone complementarity linearization algorithm. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Optimal decoupling controllers revisited

Kucera V.

Control and Cybernetics

2013

Vol. 42, no. 1

139--154

The problem of decoupling a linear system by dynamic compensation into multi-input multi-output subsystems is studied by applying proper and stable fractional representations of transfer matrices. A necessary and sufficient condition is given for a decoupling and a stabilizing controller to exist. The set of all controllers that decouple and simultaneously stabilize the system is determined in parametric form. Optimal decoupling controllers are then obtained by an appropriate selection of the parameter.