Weighted $$\mathbf{H}_\infty$$ Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method

2020 ◽  
Vol 22 (5) ◽  
pp. 1454-1467
Author(s):  
Xiushan Jiang ◽  
Senping Tian ◽  
Weihai Zhang
Keyword(s):  
Performance Analysis ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Average Dwell Time Method

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 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.

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.

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