论文标题
Lyapunov功能的近似值用于ISS分析一类非线性抛物线PDE
Approximations of Lyapunov functions for ISS analysis of a class of nonlinear parabolic PDEs
论文作者
论文摘要
本文通过不同类型的边界干扰（Robin或Neumann或dirichlet）的一类非线性高维抛物线偏微分方程（PDE）的输入到州稳定性（ISS）和积分输入对国家稳定性（IISS）涉及来自不同空间的不同类型的边界干扰（PDE）。具体而言，通过构建（强制性和非矫正）ISS lyapunov功能的近似值，我们可以建立：（i）ISS和IISS $ l^1 $ -norm（和加权$ l^1 $ -NORM）的PDES，并对$ l^q_} {loc}（\ noc} $ Q {r} $ Q { [1，+\ infty] $; （ii）$ l^1 $ -norm（和加权$ l^1 $ -norm）的PDE，带有$ l^φ__{loc}的边界干扰（\ Mathbb {r} _+; l^_+; l^1（\partialΩ）$ - 用于某些Young函数$φ$φ$;; （iii）$ l^φ$ -NORM（和加权$k_φ$ -class）的ISS和IISS，用于$ l^q_ {loc}（\ Mathbb {r} _+;k_φ（\partialΩ））$ l^q_ Q_ {loc}（\ mathbb {r} loc}（\ mathbb {\partialΩ））$ in [1，+q \ in [1，+elffty infty infty infty in] $ qulty和某些$ q $ $ q $ qungim-和ins+n yound qung。在Orlicz Space或Orlicz类的框架中评估了（II）和（III）中所述的ISS属性。
This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equations (PDEs) with different types of boundary disturbances (Robin or Neumann or Dirichlet) from different spaces by means of approximations of Lyapunov functions. Specifically, by constructing approximations of (coercive and non-coercive) ISS Lyapunov functions we establish: (i) the ISS and iISS in $L^1$-norm (and weighted $L^1$-norm) for PDEs with boundary disturbances from $L^q_{loc}(\mathbb{R}_+;L^1(\partialΩ))$-space for any $q\in [1,+\infty]$; (ii) the iISS in $L^1$-norm (and weighted $L^1$-norm) for PDEs with boundary disturbances from $L^Φ_{loc}(\mathbb{R}_+;L^1(\partialΩ))$-space for certain Young function $Φ$; and (iii) the ISS and iISS in $L^Φ$-norm (and weighted $K_Φ$-class) for PDEs with boundary disturbances from $L^q_{loc}(\mathbb{R}_+;K_Φ(\partialΩ))$-class for any $q\in [1,+\infty]$ and certain Young function $Φ$. The ISS properties stated in (ii) and (iii) are assessed in the framework of Orlicz space or Orlicz class.
