SCIENCE CHINA Information Sciences, Volume 62, Issue 9: 192201(2019) https://doi.org/10.1007/s11432-018-9557-x

## Stochastic stabilization using aperiodically sampled measurements

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• ReceivedApr 1, 2018
• AcceptedAug 3, 2018
• PublishedJul 30, 2019
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### Abstract

This paper addresses the stabilization problem of sector-bounded nonlinear systems with sampled measurements via discrete-time stochastic feedback control. Unlike the previous studies, the closed-loop system is modeled as an impulsive stochastic differential equation. By developing a quasi-periodic polynomial Lyapunov function and sampling-time-dependent Lyapunov function based methods, two sufficient conditions for almost sure exponential stability are derived in terms of differential matrix inequalities (DMIs) and linear matrix inequalities (LMIs). It is shown that the DMI-based conditions can be formulated as a sum of squares (SOSs). Moreover, the obtained results are adapted to sampled-data stochastic/deterministic systems. The numerical examples illustrate the theoretical results.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61873099, 61733008, 61573156), and Scholarship from China Scholarship Council (Grant No. 201806150120). The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

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• Figure 3

(Color online) Sample-path trajectories of stochastic system described in Example 4.2under sampled-data control law with $K=1$ and $\{t_k\}_{k\in\mathbb{N}_0}\in\mathcal{S}(0.3,1.48)$.

• Table 1   The maximum values of sampling period $\sigma_{0}$ for different $N$
 Theorem $N$ or ${\rm~deg}(P(\sigma))$ 2 4 6 10 100 Theorem 3.1 $0.061$ $0.086$ $0.086$ $0.086$ 0.086 Theorem 3.4 $0.048$ $0.062$ $0.068$ $0.075$ $0.085$
• Table 2   The maximum values of $\sigma_{1}$ for different approaches
 $\sigma_0$ Result Theorem 2 of [29] Theorem 3.4 Theorem 3.1 $\sigma_0=0.21$ $0.43$ $0.60$ $0.72$ $\sigma_0=0.40$ $1.25$ $1.64$ $1.82$ $\sigma_0=1.25$ $1.57$ $1.96$ $2.02$
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