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In this paper, we propose an explicit formula for bounded continuous feedback laws taking values in the hyperbox U := [−r− 1 , r 1 ] × · · · × [−r− m, r m], that renders an affine system globally asymptotically stable. The case of bounded positive feedback controls (r− i = 0, for i = 1, . . . ,m) is also included.
In this paper we study a kind of even degree polynomials of a special form. Necessary and sufficient conditions are given in order to decide if such polynomials have all their roots on the unit circle. Next, we apply these results to obtain sufficient conditions to have the Schur stability of a segment of polynomials.
Our main aim in this work is to study how to render an affine control system globally asymptotically stable (GAS), when the control value set (CVS) is given by an mhyperbox B r (∞) := [−r− 1 , r + 1 ] × · · · × [−r− m, r m] with 0 ∈ B r (∞). Hence we allow the null-control input in its boundary, 0 ∈ ∂B r (∞), i.e. positive/signed control input components.… (More)