scholarly journals Robust Stabilization of Linear Switched Systems with Unstable Subsystems

2018 ◽  
Vol 8 (12) ◽  
pp. 2620 ◽  
Author(s):  
Martín-Antonio Rodríguez-Licea ◽  
Francisco-J. Perez-Pinal ◽  
Juan Prado Olivares
Keyword(s):  
Switched Systems ◽  
Dwell Time ◽  
Robust Stabilization ◽  
Average Dwell Time ◽  
Time Varying ◽  
Switched Linear System ◽  
Time Switching ◽  
Switching Law ◽  
Unstable Subsystems ◽  
Average Dwell Time Switching

This paper deals with the robust stability of a class of uncertain switched systems with possibly unstable linear subsystems. In particular, conditions for global uniform exponential stability are presented. In addition, a procedure to design a mode dependent average dwell time switching signal that stabilizes a switched linear system composed of diagonalizable subsystems is established, even if all of them are stable/unstable and time-varying (within design bounds). An illustrative example of the stabilizing switching law design and numerical results are presented.

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.

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