Pure Mathematics
Vol.4 No.03(2014), Article ID:13551,8 pages
DOI:10.12677/PM.2014.43012

Stability Analysis of Uncertain Sampled-Data Systems

Rong Jia, Caixia Gao

School of Mathematical Sciences, Inner Mongolia University, Hohhot

Email: jiarong0719@126.com, gaocx0471@163.com

Received: Mar. 6th, 2014; revised: Apr. 8th, 2014; accepted: Apr. 16th, 2014

ABSTRACT

This paper deals with the stability of linear time-invariant impulsive system with feedback control. The pulses, at some time in the past, were the important factor causing system instability. Here, we first regard the impulsive system as a special reset system, then we analyze the stability of sampled-data system, and design reset matrices such that the uncertain sampled-data system is stable. Based on the classical Lyapunov method and linear matrix inequality LMI form, the necessary and sufficient conditions for stability are given. At last, we apply the results to the uncertain LTI sampled-data systems and illustrate a numerical example.

Keywords:Impulsive System, Reset Design, Sampled-Data System, Stability, Lyapunov Functions, Polytopic Embedding

1. 引言

2. 预备知识

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3. 主要结果

3.1. 稳定性分析

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3.2. 脉冲重置设计

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3.3. 算例

4. 结论

Figure 1. Constant sampling interval 1.3277

Figure 2. Varying sampling interval [0 1.1137]

Figure 3. Unstable without reset

Figure 4. Stable without reset

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