scholarly journals Decentralized Observer Based Exponential Stabilization for Linear Time-Invariant Interconnected Systems

2020 ◽  
Vol 1519 ◽  
pp. 012025
Author(s):  
Dan-Hong Hu ◽  
Zheng-Ji Mao
Keyword(s):  
Linear Time ◽  
Interconnected Systems ◽  
Exponential Stabilization ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Decentralized Observer

scholarly journals Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 853
Author(s):  
Vasilii Zaitsev ◽  
Inna Kim
Keyword(s):  
Differential Equation ◽  
Decay Rate ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Time Varying ◽  
Static State ◽  
Linear Time Invariant ◽  
Linear Differential ◽  
Time Invariant

We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or output feedback with constant gain coefficients is studied. We prove that every system is exponentially stabilizable with any pregiven decay rate by linear time-invariant static state feedback. The proof is based on the Levin’s theorem on sufficient conditions for absolute non-oscillatory stability of solutions to a linear differential equation. We obtain sufficient conditions of exponential stabilization with any pregiven decay rate for a linear differential equation with uncertain bounded coefficients by linear time-invariant static output feedback. Illustrative examples are considered.

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