Robust H_∞ Control Of Singular Time-delay Systems: Delay Decomposition Approach

Singular time-delay systems, which are also referred to as descriptor time-delay systems or generalized differential- difference equations, are matrix delay differential equations coupled with matrix difference equations. Since such systems have both delay and difference constraint, the problem of analysis and synthesis for singular time-delay systems is much more complicated than that for standard state-space time-delay systems or singular systems.H∞control is an important method in the field of system control. The main idea is to design a eontroller to stabilize the system and guarantee that the H∞norm of the transfer function from the disturbance input to the controlled output satisfies a prescribed H∞performance index.In the investigation of the delay-dependent control problems of time-delay svstems, to reduce the conservatism of the obtained results, many efforts have been made in the literature, among which the model transformation technique and bound-ing technique on cross-product terms are often used. Although the above techniques are much more well-rounded than before, the results are still conservative. So a new approach-delay decomposition approach is proposed to deal with the problem [1]. The idea of the approach is that the delay interval is uniformly divided intoⅣseg-ments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functional. For singular time-delay systems, [3] constructs a new Lyapunov-Krasovskii functional: and an improved delay-dependent stability criterion is obtained. Numerical example demonstrates that as N increases, the results converge to the analytical delay limit for stability.In this paper, by using the delay decomposition approach, the problem of delay- dependent robust H∞control for singular time-delay systems is investigated. We eonsider the system: All the coefficient matrices except the matrix E include uncertainties. The de-lay is single constant delay whose exact value is unknown. Firstly, based on the functional (1), the delay-dependent condition for singular time-delay systems is es-tablished, which guarantees that the time-delay systems is regular, impulse free, robustly internal stable and satisfies a prescribed H∞performance index. Based on the results of robust performance analysis, the existence condition of the H∞, state feedback controller is established in terms of linear matrix inequalities. Finally. an examples is given to illustrate the effectiveness of the proposed method.