On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays
TL;DR: A novel robust stability criterion under arbitrary switching signals is derived by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties and a generalization for switched nonlinear systems with multiple delays is proposed.
Abstract: This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.
Citations
More filters
Journal Article•
28,685 citations
TL;DR: Based on the constrained robust model predictive control method and an appropriate Lyapunov–Krasovskii functional, the sufficient conditions to guarantee the asymptotical stability of the switched system are developed as linear matrix inequalities.
Abstract: This paper studies the problem of robust stabilization for a class of nonlinear discrete-time switched systems with polytopic uncertainties and unknown state delay. Moreover, the control signal is ...
19 citations
TL;DR: This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays.
Abstract: This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more ge...
4 citations
Cites background from "On Robust Stability Analysis of Unc..."
...In the literature, various approaches have been proposed to study the stability analysis and the feedback stabilization of discrete-time switched time-delay systems (Aleksandrov and Mason, 2014; Aminsafaee and Shafiei,2019; ; Baleghi and Shafiei, 2018, 2019; Jaballi et al., 2016a, 2016b, 2018; Kermani and Sakly, 2018; Liu et al., 2008; Sun et al., 2007; Yali et al., 2019; Zhang et al., 2008; Zhang and Yu 2009)....
[...]
...…of discrete-time switched time-delay systems (Aleksandrov and Mason, 2014; Aminsafaee and Shafiei,2019; ; Baleghi and Shafiei, 2018, 2019; Jaballi et al., 2016a, 2016b, 2018; Kermani and Sakly, 2018; Liu et al., 2008; Sun et al., 2007; Yali et al., 2019; Zhang et al., 2008; Zhang and Yu 2009)....
[...]
...The work in Kermani and Sakly (2018) has introduced an algebraic stability criterion for a class of switched nonlinear time-delay systems, based on the CLF and the M-matrix properties....
[...]
...…Shafiei, 2019; Aoun et al., 2017, 2018; Baleghi and Shafiei, 2018, 2019; Daafouz et al., 2002; Hui et al., 2020; Jaballi et al., 2016a, 2016b, 2018; Kermani and Sakly, 2015, 2017, 2018; Liberzon andMorse, 1999; Liu et al., 2008; Sakly and Kermani, 2015; Sun et al., 2007; Vu and Liberzon, 2005;…...
[...]
DOI•
19 Dec 2022
TL;DR: In this paper , a new mechanistic algorithm called Selfish Herd Optimization (SHO) is proposed to minimize a defined performance criterion that depends on the optimal switching instants to be found.
Abstract: This paper addresses the optimal control problem of switched nonlinear systems. Indeed, a new mechanistic algorithm called Selfish Herd Optimization (SHO) is suggested. The proposed approach consists of minimizing a defined performance criterion that depends on the optimal switching instants to be found. Finally, the effectiveness of the proposed approach is illustrated through a switched hydraulic two-tank nonlinear system.
References
More filters
Journal Article•
28,685 citations
TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
Abstract: By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.
3,566 citations
01 Jan 1999
TL;DR: In this article, it was shown that switching among stable linear systems results in a stable system provided that switching is slow-on-the-average, i.e., the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small.
Abstract: It is shown that switching among stable linear systems results in a stable system provided that switching is \slow-on-the-average." In particular, it is proved that exponential stability is achieved when the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.
2,028 citations