Finite-Time Input-to-State Stability and Optimization of Switched Nonlinear Systems

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Xiaoli Wang ◽  
Chuntao Shao
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Stability Problem ◽  
Stability Property ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Time Switching ◽  
Switched Nonlinear System ◽  
Average Dwell Time Switching

In this paper, we address the (uniform) finite-time input-to-state stability problem for switched nonlinear systems. We prove that a switched nonlinear system has a useful finite-time input-to-state stability property under average dwell-time switching signals if each constituent subsystem has finite-time input-to-state stability. Moreover, we prove the equivalence between the optimal costs for the switched nonlinear systems and for the relaxed differential inclusion.

scholarly journals On Exponential Stabilizability for a Class of Switched Nonlinear Systems with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jie Qi ◽  
Yuangong Sun
Keyword(s):  
Nonlinear Systems ◽  
Average Dwell Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Positive Systems ◽  
Time Switching ◽  
Switched Nonlinear System ◽  
Exponentially Stable ◽  
A New Technique ◽  
Average Dwell Time Switching

We study the exponential stabilizability for a class of switched nonlinear systems with mixed time-varying delays. By using a new technique developed for positive systems, we design the average dwell time switching under which the switched nonlinear system is exponentially stable for any bounded delays. Finally, numerical examples are worked out to illustrate the main theoretical result.

Finite-time stability and asynchronously switching control for a class of time-varying switched nonlinear systems

2019 ◽  
Vol 42 (6) ◽  
pp. 1215-1224
Author(s):  
Ronghao Wang ◽  
Jianchun Xing ◽  
Zhengrong Xiang ◽  
Qiliang Yang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Dwell Time ◽  
Autonomous Systems ◽  
Average Dwell Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Stability ◽  
Control Lyapunov Function ◽  
Finite Time Stability

Finite-time stability and stabilization for switched nonlinear systems has been investigated in the paper. Based on existing works, we find that related results on autonomous switched nonlinear systems cannot be simply extended to non-autonomous systems. A sufficient condition has been proposed for this class of systems using the average dwell time method. Specifically, a control Lyapunov function approach is employed to stabilize the system and the finite-time controller is designed using a small control property. In contrast to autonomous switched systems, a finite-time stabilizer is constructed for time-varying switched nonlinear systems, even under the situation in which the switching mode is different between the system and the controller. Furthermore, the relation between the settling time and the average dwell time has been revealed. Finally, an example case is presented for the obtained result.

Finite-time boundedness and stabilization of switched nonlinear systems using auxiliary matrices and average dwell time method

2019 ◽  
Vol 42 (7) ◽  
pp. 1406-1416 ◽  
Author(s):  
Hadi Gholami ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
System Matrix ◽  
Lyapunov Matrix ◽  
Average Dwell Time Method ◽  
Finite Time Boundedness

This paper focuses on the finite-time boundedness of switched nonlinear systems based on the Finsler’s lemma, auxiliary matrices, and average dwell time method. The analysis is provided for a switched system with Lipschitz nonlinearities and in the presence of external disturbances. Moreover, a switching controller is designed based on linear matrix inequalities (LMIs), to make the closed-loop system finite-time bounded. Presented theorems in this paper are more general and have less conservatism than the existing methods due to using the auxiliary matrices that make the Lyapunov matrix separate from the system matrix in the resulting LMIs. Moreover, in all theorems, the average dwell time of the switching system has been evaluated. Three examples are given to illustrate the effectiveness of the proposed method and to show that it is less conservative compared with existing methods.

Finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching

2014 ◽  
Vol 92 (2) ◽  
pp. 93-102 ◽  
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Fengxia Zheng ◽  
Kaibo Shi
Keyword(s):  
Finite Time ◽  
Dwell Time ◽  
Transition Probabilities ◽  
Average Dwell Time ◽  
Time Switching ◽  
Piecewise Constant ◽  
Switching Models ◽  
Finite Time Boundedness ◽  
Jump Systems ◽  
Average Dwell Time Switching

This paper investigates the problem of finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching. Another set of useful regime-switching models has been given for both fixed transition probability Markov switching models and time-varying transition probabilities. Based on the knowledge of average dwell time and multiple Lyapunov function, a novel sufficient condition for finite-time boundedness of H∞ filtering is derived and the system trajectory stays within a prescribed bound. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.

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