Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Sun Huiying; Li Meng; Ji Shenglin; Yan Long

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Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

机译：状态相关噪声的离散时间马尔可夫跳跃线性系统的稳定性和线性二次微分对策

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We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ) differential games. A necessary and sufficient condition involved with the connection between stochastic T-n-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic T-n-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs). Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

机译：我们主要考虑具有状态相关噪声的离散时间Markovian跳跃线性系统的稳定性及其线性二次（LQ）微分博弈。提出了与状态相关的马尔可夫跳跃线性系统的随机T-n稳定性与Lyapunov方程之间的联系的充要条件。并运用随机T-n稳定性理论，给出了无限水平LQ随机微分对策的最优策略和最优成本值。证明了无限水平LQ随机微分对策的求解与四个耦合广义代数Riccati方程（GAREs）有关。最后，提出了一种迭代算法来求解四个耦合的GARE，并给出了仿真示例来说明其有效性。

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来源
《Mathematical Problems in Engineering》 |2014年第21期|265621.1-265621.11|共11页
作者
Sun Huiying; Li Meng; Ji Shenglin; Yan Long;
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Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China.;

Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China.;

Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China.;

Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China.;

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1. Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise [J] . HuiyingSun, MengLi, ShenglinJi, Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第a期

机译：具有国家依赖噪声的离散时间Markovian跳跃线性系统的稳定性和线性二次差动游戏
2. The linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and Markovian jumping [J] . Dragan V., Morozan T. IEEE Transactions on Automatic Control . 2004,第5期

机译：一类带乘性白噪声和马尔可夫跳跃的线性随机系统的线性二次优化问题
3. Correction to "The linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and Markovian jumping" [J] . Dragan V., Morozan T. IEEE Transactions on Automatic Control . 2004,第10期

机译：对“乘性白噪声和马尔可夫跳跃的一类线性随机系统的线性二次优化问题”的修正
4. Linear quadratic differential games for discrete-times Markovian jump stochastic linear systems: Infinite-horizon case [C] . Sun Huiying, Feng Chunyu, Jiang Liuyang 2011 30th Chinese Control Conference . 2011

机译：离散时间马尔可夫跳跃随机线性系统的线性二次微分对策：无限水平情形
5. Stability analysis of jump-linear systems driven by finite-state machines with Markovian inputs. [D] . Patilkulkarni, Sudarshan S. 2004

机译：具有马尔可夫输入的有限状态机驱动的跳跃线性系统的稳定性分析。
6. An LMI Based Criterion for Global Asymptotic Stability of Discrete-Time State-Delayed Systems with Saturation Nonlinearities [O] . Priyanka Kokil 2014

机译：具有饱和非线性的离散状态时滞系统的全局渐近稳定性的基于LMI的准则
7. Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise [O] . Huiying Sun, Meng Li, Shenglin Ji, 2014

机译：具有国家依赖噪声的离散时间Markovian跳跃线性系统的稳定性和线性二次差动游戏

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

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