Discrete-State Decomposition Technique of Dissipativity Analysis for Discrete-Time Singular Systems With Time-Varying Delays
针对时变时滞离散奇异系统，提出离散状态分解技术，通过建立状态分解的李雅普诺夫函数并采用不等式方法，得到计算复杂度更低、保守性更小的耗散性判据，并通过仿真验证了优越性。
This article is concerned with the problem of dissipativity for discrete-time singular systems with time-varying delays. First, the discrete-state decomposition technique is proposed after performing the restricted equivalent transformation for singular systems. To reduce the use of decision variables, the state-decomposed Lyapunov function is established based on the decomposed state vectors. Second, to obtain the condition with less conservatism, the two zero-value equations, especially concerning difference subsystems and algebraic ones, the discrete Wirtinger-based inequality and the extended reciprocally convex inequality are employed to bound the forward difference of the Lyapunov function. Then, the less conservative dissipativity criteria with lower computational complexity are obtained. Finally, simulation results are provided to demonstrate the superiority of the proposed technique.