LMI-based delay-dependent robust control for value bounded uncertain systems with time delay

Abstract

The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding "zeros" matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality (LMI). LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.In the past few years, the delay dependent robust control for linear delay systems has been attracting a large number of researchers [1][2][3][4][5][6][7][8] . The model transformation approach has been widely used in the literatures [1][2][3][4] , by which a system is converted to a new system, equivalent or nonequivalent to the original system. Then the Lyapunov-Krasovskii functional and linear matrix inequality approach were used and various techniques have been introduced, based on which the delay-dependent robust stability condition and robust controller can be obtained. Based on the literature [5,6] , the Park inequality has been created by introducing the matrix decomposition into a synthesis problem, and the lower conservative design of a state feedback controller has been achieved. The method of free weighting matrices has been presented in the literatures [7,8] where the enlargement and diminution of inequality has been less used causing the results to be lower conservative. However, the matching conditions of uncertainty need to be satisfied in the above literatures. In practical engineering, the uncertainty is often value-bounded and is more universal [9] , which need not satisfy the so-called matching conditions. The research of robust controllers with value-bounded uncertainties is generally delay independent [9,10] . The delay is often value-bounded in practical engineering whereas the related research of robust controllers with value-bounded uncertainties and delay-dependent is rarely involved.In this paper, by utilizing Lyapunov-Krasovskii

An explanation of the “grey system” analysis methodology for the evaluation of inert anode materials

“…Cermet is a very interesting potential material for making inert anodes. It is composed of a ceramic phase, typically such as the spinel NiFe 2 O 4 , and a metal or alloy phase, such as Ni‐Fe‐Cu (Deng, 1988). In the work described in this paper, the ceramic phase material mainly was studied by determining its appropriate calcination temperature.…”