Singular finite horizon full information $${\mathcal H}^ \infty$$ control via reduced order Riccati equations.(English)Zbl 0863.93026

For linear time-varying systems the standard finite horizon, full information $$H_\infty$$ control problem is considered. The authors study the singular case when the direct feedthrough matrix that links the control input to the controlled output is not full column rank. Combining the game-theoretical approach and decomposition methods which are based on the concept of strongly controllable subspace and which has been used in the time-invariant singular case, the authors derive a solution for time-varying systems with continuously differentiable matrices. It is shown that the original problem is equivalent to a reduced order one, which under certain assumptions is regular and its solution can be obtained via a reduced order Riccati differential equation.

MSC:

 93B36 $$H^\infty$$-control
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References:

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