Abstract
The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.
Highlights
Singular systems are more convenient than regular ones for describing many practical systems because a singular system involves both differential equations and algebraic equations
The robust H∞ control problem for uncertain singular time-delay systems was investigated by Ji et al in [24], where the linear matrix inequality (LMI) condition was obtained by constructing a degenerate Lyapunov ed22 k< 1, which renders function on the basis of [23]
The problem of robust H∞ control is considered for the singular neutral system in Equation (1) with F (t) = 0 and u(t) = 0
Summary
Singular systems are more convenient than regular ones for describing many practical systems because a singular system involves both differential equations and algebraic equations. Scholars (such as [11,12,13,14,15]) have started to study the H∞ problem for singular time-delay systems by using a linear matrix inequality (LMI) approach, which yields the existence conditions valid for singular systems’ regular problems and characterizations of H∞ controllers, leading to a convex optimization problem [16,17,18,19,20,21,22,23,24,25,26,27,28,29]. The robust H∞ control problem for uncertain singular time-delay systems was investigated by Ji et al in [24], where the LMI condition was obtained by constructing a degenerate Lyapunov ed k< 1, which renders function on the basis of [23]. The present paper derives a sufficient condition for the existence of the H∞ controller on the basis of the LMI approach combined with a class of novel augmented Lyapunov functions, which facilitate the attainment of the H∞ controller using the Matlab LMI toolbox combined with a matrix equation
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