scholarly journals Stabilization of a Class of Continuous-Time Switched Systems with State Constraints via a Mode-Dependent Switching Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qingyu Su ◽  
Peipei Wang
Keyword(s):  
Continuous Time ◽  
Switched Systems ◽  
Dwell Time ◽  
State Constraints ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Decay Rates ◽  
Average Dwell Time Method ◽  
The Stability ◽  
Switching Method

The stability and the stabilization problems for a class of continuous-time switched systems with state constraints via a mode-dependent switching method are investigated. The paper presents an improved average dwell time method, which considers different decay rates of a Lyapunov function related to each of the active subsystems according to whether the saturations occur or not, respectively. It is shown that the improved average dwell time method is less conservative than the common average dwell time method. Based on the improved average dwell time method, the sufficient conditions and state feedback controllers for stabilization of the switched system are derived. A numerical example is given to illustrate the proposed approach.

H∞ control for a class of continuous-time switched systems with state constraints via a mode-dependent switching method

2018 ◽  
Vol 40 (11) ◽  
pp. 3358-3367 ◽  
Author(s):  
Qingyu Su ◽  
Haichao Zhu ◽  
Jian Li
Keyword(s):  
Switched Systems ◽  
Dwell Time ◽  
State Feedback ◽  
State Constraints ◽  
Average Dwell Time ◽  
Decay Rates ◽  
Globally Asymptotically Stable ◽  
Average Dwell Time Method ◽  
Linear State ◽  
Switching Method

In this paper, the H∞ control problem for linear state-constrained switched systems via the improved mode-dependent average dwell time method is investigated. Using this proposed method, which considers different decay rates of a Lyapunov function related to an active subsystem on the basis of whether there is saturation or not, the resulting minimum admissible mode-dependent average dwell time is smaller than that of the traditional average dwell time method, which assumes a constant decay rate, regardless of whether there is saturation or not. Thus, this method is less conservative than the traditional average dwell time method. In addition, this paper outlines the design of the state feedback controller of the switched systems, which guarantees that the closed-loop linear state-constrained switched system is globally asymptotically stable and obtains a weighted L2 gain. The availability and applicability of the proposed method are shown by the application of a boost converter.

scholarly journals Stability Analysis of a Class of Switched Nonlinear Systems with an Improved Average Dwell Time Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongwei Guo
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Asymptotically Stable ◽  
Switched Nonlinear Systems ◽  
Globally Asymptotically Stable ◽  
Unstable Subsystems ◽  
Average Dwell Time Method ◽  
The Stability

This paper investigates the stability of switched nonlinear (SN) systems in two cases: (1) all subsystems are globally asymptotically stable (GAS), and (2) both GAS subsystems and unstable subsystems coexist, and it proposes a number of new results on the stability analysis. Firstly, an improved average dwell time (ADT) method is presented for the stability of such switched system by extending our previous dwell time method. In particular, an improved mode-dependent average dwell time (MDADT) method for the switched systems whose subsystems are quadratically stable (QS) is also obtained. Secondly, based on the improved ADT and MDADT methods, several new results to the stability analysis are obtained. It should be pointed out that the obtained results have two advantages over the existing ones; one is that the improved ADT method simplifies the conditions of the existing ADT method, the other is that the obtained lower bound of ADT (τa*) is also smaller than that obtained by other methods. Finally, illustrative examples are given to show the correctness and the effectiveness of the proposed methods.

Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs

2016 ◽  
Vol 40 (4) ◽  
pp. 1082-1091 ◽  
Author(s):  
Junqi Yang ◽  
Yantao Chen ◽  
Zheng Zheng ◽  
Wei Qian
Keyword(s):  
State Estimation ◽  
Switched Systems ◽  
Dwell Time ◽  
Sliding Mode ◽  
Lipschitz Constant ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Nonlinear Switched Systems ◽  
Continuous State

This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

scholarly journals Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Li ◽  
Xiaodi Li ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Switched Systems ◽  
Dwell Time ◽  
Lyapunov Method ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Nonlinear Switched Systems

This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

scholarly journals Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang
Keyword(s):  
Exponential Stability ◽  
Robust Stability ◽  
Integral Inequality ◽  
Global Exponential Stability ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Asynchronous Switching ◽  
Average Dwell Time Method

The problem of robust stability of switched delay systems with average dwell time under asynchronous switching is investigated. By taking advantage of the average dwell-time method and an integral inequality, two sufficient conditions are developed to guarantee the global exponential stability of the considered switched system. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.

New stabilization results for discrete-time positive switched systems with forward mode-dependent average dwell time

2016 ◽  
Vol 39 (2) ◽  
pp. 224-229 ◽  
Author(s):  
Tingting Liu ◽  
Baowei Wu ◽  
Yue-E Wang ◽  
Lili Liu
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Stability Result ◽  
Average Dwell Time ◽  
Feedback Controllers ◽  
Multiple Sample ◽  
The Stability ◽  
Positive Switched Systems ◽  
Time Linear

The stability and stabilization of discrete-time linear positive switched systems are discussed in this paper. First, based on the concept of the forward mode-dependent average dwell time, a stability result for discrete-time linear positive switched systems is obtained by utilizing the multiple linear copositive Lyapunov functions. Then, by introducing multiple-sample Lyapunov-like functions variation, a new exponential stability result is derived. Finally, the conditions for the existence of mode-dependent stabilizing state feedback controllers are investigated, and two illustrative examples are given to show the correctness of the theoretical results obtained.

Stability analysis of switched systems with extended average dwell time

2017 ◽  
Vol 40 (5) ◽  
pp. 1425-1434 ◽  
Author(s):  
Qiang Yu ◽  
Yunfei Yin ◽  
Xudong Zhao
Keyword(s):  
Stability Analysis ◽  
Continuous Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
The Other ◽  
Open Chain ◽  
Closed Chain ◽  
Special Cases ◽  
Stability And Stabilization

The problem of stability for switched systems with extended average dwell time (ADT) is investigated in both the continuous-time and discrete-time cases. By proposing three novel concepts of closed-chain, r-open-chain, and quasi-cyclic switching signals, stability and stabilization conditions of switched systems with ADT or mode-dependent ADT (MDADT) switching are obtained. This paper develops and enriches the existing results on stability under constrained switching, since the existing results based on both ADT and MDADT can be seen as the special cases of ours. On the other hand, the paper provides a solution to the open problem of how to obtain a tighter bound on ADT or MDADT. Finally, some comparisons between the existing results and ours show the superiority of the theoretical findings of this paper.

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