Abstract
This paper investigates the state feedback stabilization problem for a class of impulsive linear time-varying systems over specified time intervals and piecewise quadratic domains (PQDs). First, concepts related to finite-time stability and PQDs are given. Second, finite-time stability analysis over PQDs is implemented, and a variety of stability conditions involving differential linear matrix inequalities are investigated. Then, computationally tractable stability conditions are established for the control design. Finally, an illustrative example is presented to show the effectiveness of the designed state feedback control.
Highlights
Finite-time stability and stabilization are of importance in the applied mathematics and control fields and become a growing cross-disciplinary research area in the past decades.ey can be found useful in a variety of applications; for example, when a rocket is launched, it should be controlled to stay in a specified region after a given time interval
Ey can be found useful in a variety of applications; for example, when a rocket is launched, it should be controlled to stay in a specified region after a given time interval
We are interested in the finite-time stability and stabilization problems of impulsive linear systems in the quantitative sense. e system trajectory evolves in restrained regions during a specified interval of time. e concept of finite-time stability is different from that in the qualitative sense [4, 5], which emphasizes that the asymptotically stable system is capable to reach the equilibrium at the settling time
Summary
Finite-time stability and stabilization are of importance in the applied mathematics and control fields and become a growing cross-disciplinary research area in the past decades. We are interested in the finite-time stability and stabilization problems of impulsive linear systems in the quantitative sense. Is paper investigates the state feedback finite-time stabilization problem for an impulsive linear system. Comparing with previous work in [18, 19, 22], this paper has the following main contributions: (1) notions of piecewise quadratic functions and piecewise quadratic domains have been extended to impulsive linear time-varying systems; (2) computationally tractable sufficient conditions for finite-time stability with PQDs are established; and (3) efficient state feedback control to stabilize impulsive linear systems with respect to PQDs is designed.
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