Stability analysis of a class of uncertain switched time‐delay systems with sliding modes

Abstract

Summary This paper presents sufficient conditions to ensure the exponential stability of uncertain switched time‐delay systems with time‐delayed state‐dependent switching conditions, which can model high speed supercavitation vehicles (HSSVs). Based on the intrinsic properties of HSSVs, cavity can be represented by a relation between the states and time‐delayed states of the system. Moreover, a sliding behavior can be occurred at the cavity boundary in HSSVs. Therefore, the main contribution of this paper is to develop a set of LMI stability conditions in the presence of time‐delayed states in the linear state‐dependent switching signal and absorbing sliding modes in the state space, simultaneously. In addition, because of the possible existing uncertainties in HSSVs, another set of LMI‐based sufficient conditions is derived in order to analyze the stability of switched time‐delay systems with additive norm bounded uncertainties. The application of the proposed theorems are also validated through numerical examples. Finally, the stability of a two‐degrees‐of‐freedom longitudinal description of an HSSV is shown using the proposed stability theorems.

Static output feedback control of switched nonlinear systems with time-varying delay and parametric uncertainties under asynchronous switching

“…Based on a switched Lyapunov function, state feedback and static output controllers have been designed in the framework of linear matrix inequalities (LMIs) for robust stabilization of uncertain discrete-time switched singular systems (Chadli and Darouach, 2011). In the case of uncertain switched systems with time-delay, the majority of the results are based on polytopic or norm-bounded uncertainties (Aminsafaee and Shafiei, 2019; Kani et al, 2019; Sun et al, 2006). On the other hand, there exists another type of uncertainty called parametric uncertainty, which is more compatible with practical systems (Baleghi and Shafiei, 2018c; Zhai et al, 2012).…”

Event-Driven Control for Switched Systems With Quantization and Packet Loss

“…D Uring the past few decades, switched systems, one special class of hybrid systems, have been widely investigated and many useful results have been obtained (see, for example [1][2][3][4][5][6][7]). If the data of a switched system is transmitted through the network, then the controller design will subject to the effect of quantization (caused by limited communication rate), delay and packet loss (caused by network congestion).…”

Sliding mode control of discrete‐time switched systems subject to mode delays

“…Owing to the significance both in practical applications and theoretical research, switched systems have been widely investigated in many fields, such as robotics, power electronics, chemical processes, aircraft and air traffic control, etc, and lots of exciting results have been obtained on the stability and stabilization problems for switched systems in the past decade . Especially, sliding mode control (SMC) method, as an effective robust control technique, has been also successfully applied in uncertain switched systems, stochastic systems, and other systems . For example, the SMC problem was considered in the work of Wu and Lam for uncertain switched systems with the same control input matrices for all subsystems.…”