Linear quadratic control with stability degree constraint

Abstract The problem of static state feedback Linear Quadratic (LQ) optimal control subject to a prescribed degree of stability for the closed-loop system is considered in this paper. A necessary optimality condition is given via the Lagrange multiplier method. A globally convergent algorithm is provided to solve the optimization problem. It is shown that the algorithm recovers the standard LQ feedback gain provided the desired stability degree is small enough to be within the range by the standard LQ design. As for other cases the optimum occurs on the boundary of the α-region. A numerical example shows that the proposed algorithm provides a better design compared to the existing methods.

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