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首页> 外文期刊>IEEE Transactions on Automatic Control >On Boundedness of Solutions of State Periodic Systems: A Multivariable Cell Structure Approach
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On Boundedness of Solutions of State Periodic Systems: A Multivariable Cell Structure Approach

机译：状态周期系统解的有界性：多变量单元结构方法

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摘要

Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function, the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability, i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system.
机译：关于许多状态变量，许多动力学系统是周期性的。此周期性通常会导致多个不变解（平衡或极限环）共存。结果，尽管有许多经典的技术可用于分析此类系统的有界性和稳定性，但其中大多数只允许建立局部属性。因此，提出了一种新的充分的准则来解决这类非线性系统解的整体有界性。拟议的方法受到Leonov和Noldus开发的细胞结构方法的启发，并具有两个主要进展。首先，常规单元结构框架扩展到动态情况，动态情况相对于多个状态是周期性的。其次，通过引入Leonov函数的概念，标准Lyapunov函数的通常确定性要求被放宽为符号不确定函数。此外，表明在（轻微）附加条件下，列昂诺夫函数的存在还确保了输入到状态的稳定性，即相对于外来扰动的鲁棒性。通过对非线性系统的轨迹有界性进行全局分析，证明了该方法的性能。

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