An Observer for a class of Bilinear Systems with Multi-Output Signal

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  • 多出力をもつある双線形システムに対するオブザーバ
  • タ シュツリョク オ モツ アル ソウセンケイ システム ニ タイスル オブザ

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This paper presents a method to construct an observer for the bilinear systems with m-output signal, described by S1;x(k+1)=up(k)Ax(k)+Bu(k), y(k)=Cx(k) where x(k)∈Rn, u(k)≜(u1(k)，……,　up(k)，……ur(k))T ∈Rr, y∈Rm. And it is assumed here that S1 is observable and matrix A is non-singular. The observer of S1 proposed here is S0; z(k+1)=up(k) UAJz(k)+UAGy(k)up(k)+UBu(k), x(k)=Jz(k)+Gy(k), where z(k)∈Rl and x(k) is the estimated value of x(k). It is shown that i). the dimension of S1 is minimal if l=n-m. ii) an example of the solutions such that S0 is the minimal order observer of S1 is given by a g-inverse of C, and iii) then x(k) and x(k) become identical by the adjustment of β-1 steps, where β is observability index of S1.

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