The sum-of-squares problem and dissipative systems

被引：0
|
作者：
Willems, JC [1 ]
Pillai, HK [1 ]
机构：
[1] Katholieke Univ Leuven, Louvain, Belgium
来源：
Fourth International Workshop on Multidimensional Systems - NDS 2005 | 2005年
关键词：
D O I：
10.1109/NDS.2005.195329
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this presentation, we discuss the theory of dissipativeness of systems described by linear constant coefficient PDE's with respect to supply rates that are quadratic differential forms in the variables and their derivatives. The main issue considered is the equivalence of global and local dissipativeness. This leads to the construction of the storage function, the flux, and the dissipation rate. We show that mathematically this leads to Hilbert's 17-th problem on the factorization of a polynomial in n variables as a sum of squares.
引用
收藏
页码：48 / 53
页数：6
相关论文
共 50 条
  • [41] On the conservatism of the sum-of-squares method for analysis of time-delayed systems
    Peet, Matthew M.
    Bliman, Pierre-Alexandre
    AUTOMATICA, 2011, 47 (11) : 2406 - 2411
  • [42] A Sum-of-Squares Approach to the Analysis of Zeno Stability in Polynomial Hybrid Systems
    Murti, Chaitanya
    Peet, Matthew
    2013 EUROPEAN CONTROL CONFERENCE (ECC), 2013, : 1657 - 1662
  • [43] Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization
    Fantuzzi, G.
    Goluskin, D.
    Huang, D.
    Chernyshenko, S. I.
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2016, 15 (04): : 1962 - 1988
  • [44] Mixed-integer programming techniques for the minimum sum-of-squares clustering problem
    Burgard, Jan Pablo
    Moreira Costa, Carina
    Hojny, Christopher
    Kleinert, Thomas
    Schmidt, Martin
    JOURNAL OF GLOBAL OPTIMIZATION, 2023, 87 (01) : 133 - 189
  • [45] Mixed-integer programming techniques for the minimum sum-of-squares clustering problem
    Jan Pablo Burgard
    Carina Moreira Costa
    Christopher Hojny
    Thomas Kleinert
    Martin Schmidt
    Journal of Global Optimization, 2023, 87 : 133 - 189
  • [46] Fault tolerant control for nonlinear systems: Sum-of-squares optimization approach
    Ma, Hong-Jun
    Yang, Guang-Hong
    PROCEEDINGS OF THE 2007 IEEE CONFERENCE ON CONTROL APPLICATIONS, VOLS 1-3, 2007, : 435 - 440
  • [47] Optimal Control for a Class of Chaotic Systems Using Sum-of-Squares Programming
    Zhu Gui
    Lou Xuyang
    Qiu Fang
    PROCEEDINGS OF THE 38TH CHINESE CONTROL CONFERENCE (CCC), 2019, : 1851 - 1855
  • [48] Reducing the Complexity of the Sum-of-Squares Test for Stability of Delayed Linear Systems
    Zhang, Yashun
    Peet, Matthew
    Gu, Keqin
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (01) : 229 - 234
  • [49] An Iterative Sum-of-Squares Optimization for Static Output Feedback of Polynomial Systems
    Baldi, Simone
    2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC), 2016, : 3892 - 3897
  • [50] Applying Sum-of-Squares Decomposition Technique to Power System Robust Control Problem
    Chen, Mingyuan
    Li, Xiaocong
    Lagoa, Constantino M.
    Cong, Lanmei
    Xu, Junhua
    IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, 2018, 13 (02) : 218 - 225
12345