Stability Analysis and Controller Design With Less Conservatism for Singular Networked Control Systems With Short Time-Varying Delay

This paper investigates the issue of reducing conservatism in stability analyses and controller design for singular networked control systems (SNCSs) with short time-varying delays. The shortcomings and its causes of existing research on related SNCSs are analyzed. By constructing augmented state equations and considering the effect of time delays, the SNCSs are modeled as linear discrete systems with parameter uncertainties, and the bound of uncertainties is obtained based on the nominal point method. A more universal quadratic Lyapunov functional is selected for the stability analysis and controller design. Based on Lyapunov stability theory, a sufficient condition for asymptotic stability is proposed in the form of linear matrix inequalities (LMIs), and design methods for a guaranteed cost controller and an optimal H $\infty $ controller are proposed. The numerical example shows that the proposed method can effectively reduce conservatism and improve the performance index compared with the existing method, thus, the application scenarios can be expanded.