Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates

Kao Y.; Xie J.; Wang C.

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Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates

机译：具有不确定跃迁率的奇异马氏跳跃系统的镇定。

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摘要

This note is devoted to investigating the stability and stabilization problems for continuous-time singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). In this GUTR singular model, each transition rate can be completely unknown or only its estimate value is known. In terms of a set of coupled linear matrix inequalities (LMIs), a sufficient condition is established to ensure the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent state-feedback controller is derived to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.

机译：本说明专门研究具有通常不确定的跃迁速率（GUTR）的连续时间奇异马尔可夫跳跃系统（SMJS）的稳定性和稳定问题。在这个GUTR奇异模型中，每个跃迁速率可能是完全未知的，或者只有其估计值是已知的。根据一组耦合的线性矩阵不等式（LMI），建立了充分的条件以确保系统规则，无脉冲且随机稳定。此外，通过应用LMI技术，推导了存在依赖于模式的状态反馈控制器的相应充分条件，以确保闭环系统可以随机地被接受。最后，通过算例说明了该方法的有效性和有效性。

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《Automatic Control, IEEE Transactions on》 |2014年第9期|2604-2610|共7页
作者
Kao Y.; Xie J.; Wang C.;
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正文语种 eng
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Closed loop systems; Linear matrix inequalities; Numerical stability; Stability criteria; Stochastic processes; Symmetric matrices; Generally uncertain transition rate (TR); singular Markovian jump system (MJS); stochastic admissibility; stochastic stability;

机译：闭环系统;线性矩阵不等式;数值稳定性;稳定性标准;随机过程;对称矩阵通常不确定的过渡率（TR）;奇异马尔可夫跳跃系统（MJS）;随机可接纳性;随机稳定性;

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机译：具有不确定转换率的奇异切换半马氏跳跃系统的稳定性与镇定。
2. H_∞ Filtering for Discrete-Time Singular Markovian Jump Systems with Generally Uncertain Transition Rates [J] . Shen Anyou, Li Lin, Li Chunyu Circuits, systems and signal processing . 2021,第7期

机译：H_∞过滤离散时间单数Markovian跳跃系统，具有通常不确定的过渡率
3. Asynchronous adaptive dynamic output feedback sliding mode control for singular markovian jump systems with actuator faults and uncertain transition rates [J] . Applied mathematics and computation . 2020,第期

机译：异步自适应动态输出反馈滑动模式控制与执行器故障的单数马尔维亚跳跃系统和不确定的过渡率
4. Output feedback stabilization of stochastic linear systems with Markovian switching and uncertain transition jump rates [C] . Dawei Xiao, Junyong Zhai, Wenting Zha, Chinese Control Conference . 2015

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5. Robustness analysis of uncertain linear systems and robust stabilization of uncertain delayed systems. [D] . Basker, Varadharajan Radhamani. 1998

机译：不确定线性系统的鲁棒性分析和不确定延迟系统的鲁棒稳定性。
6. Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage mixed time delays and α-inverse Hölder activation functions [O] . C. Maharajan, R. Raja, Jinde Cao, -1

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7. Stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities [O] . Wang Jianhua, Zhang Qingling, Yan Xinggang, 2015

机译：转移概率部分未知的离散时间奇异马尔可夫跳跃系统的随机稳定性和稳定性
8. Markovian Decision Processes with Uncertain Transition Probabilities [R] . Gozzolino, J. M., Gonzalez-Zubieta, R., Miller, R. L. 1965

机译：具有不确定转移概率的马尔可夫决策过程

Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates

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