Control for a class of second-order systems via a state-dependent riccati equation approach

Li Gang Lin, Yew Wen Liang, Li Jen Cheng

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This study investigates the state-dependent Riccati equation (SDRE) controller for a class of second-order nonlinear systems. By fully exploiting the design degree of freedom (DOF) arising from the nonunique state-dependent coefficient (SDC) matrices, we explicitly calculate the ranges of control input via the SDRE scheme. Moreover, when a permissible control input is determined, we also explicitly parameterize the SDC matrices that result in the designated control value, in terms of system States and parameters, so the engineer can easily implement the scheme. Notably, this is the first analytical result that explores the range of control input using the design DOF of SDC matrices. In addition, by applying the analytical results, it is shown that the second-order systems are always globally stabilizable, without any supplementary assumptions on weighting matrices (as extended from existing SDRE global results), and the corresponding stabilizing SDC matrices are also explicitly presented. Finally, illustrative examples clearly demonstrate the benefits of the analytical results.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalSIAM Journal on Control and Optimization
Issue number1
StatePublished - 2018


  • Globally asymptotic stability
  • Nonlinear control system
  • State-dependent coefficient matrix
  • State-dependent riccati equation


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