## Decoupling of square singular systems via proportional state feedback.(English)Zbl 0726.93013

The author presents necessary and sufficient conditions for the decoupling of a solvable square singular system $$E\dot x(t)=Ax(t)+Bu(t)$$ with output $$y=Dx(t)$$, via an admissible control law of the form $$u(t)=Kx(t)+Hr(t)$$ (where H is a square nonsingular matrix). He shows that there exists a proportional state feedback for which the system’s transfer function is a diagonal, nonsingular and proper rational matrix. The proofs of the main results are constructive and provide a procedure for computing an appropriate proportional state feedback.
Reviewer: S.Anita (Iaşi)

### MSC:

 93B11 System structure simplification 93C05 Linear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 93C99 Model systems in control theory 34A09 Implicit ordinary differential equations, differential-algebraic equations

### Keywords:

square singular system; state feedback; time-invariant
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