|
Kalman's conjecture or Kalman problem is a disproved conjecture on absolute stability of nonlinear control system with one scalar nonlinearity, which belongs to the sector of linear stability. Kalman's conjecture is a strengthening of Aizerman's conjecture and is a special case of Markus–Yamabe conjecture. This conjecture was proven false but led to the (valid) sufficient criteria on absolute stability. == Mathematical statement of Kalman's conjecture (Kalman problem)== In 1957 R. E. Kalman in his paper 〔 〕 stated the following:
Kalman's statement can be reformulated in the following conjecture:〔 〕
In Aizerman's conjecture in place of the condition on the derivative of nonlinearity it is required that the nonlinearity itself belongs to the linear sector. Kalman's conjecture is true for ''n'' ≤ 3 and for ''n'' > 3 there are effective methods for construction of counterexamples:〔 〕〔 〕 the nonlinearity derivative belongs to the sector of linear stability, and a unique stable equilibrium coexists with a stable periodic solution (hidden oscillation). In discrete-time, the Kalman conjecture is only true for n=1, counterexamples for ''n'' ≥ 2 can be constructed.〔 〕〔 〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kalman's conjecture」の詳細全文を読む スポンサード リンク
|