Exponential stability of discrete-time linear singular positive time-delay systems

2015 ◽  
Author(s):  
Liu Tingting ◽  
Wu Baowei ◽  
Tong Yunxu
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Discrete Time ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Positive Time ◽  
Time Linear

scholarly journals Exponential Estimates and Stabilization of Discrete-Time Singular Time-Delay Systems Subject to Actuator Saturation

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Jinxing Lin
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Decay Rate ◽  
Discrete Time ◽  
Actuator Saturation ◽  
Singular Systems ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Exponential Estimates ◽  
Singular Time

This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

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