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We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...
A circle criterion is obtained for a SISO Lur’e feedback control system consist- ing of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previ- ously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the trans- fer function belongs...
A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results...
A corrected version of [P. Grabowski and F.M. Callier,
(2006) 169–197], Theorem 4.1, p. 186, and Example, is given.
A Lur'e feedback control system consisting of a linear, infinite-dimensional
system of boundary control in factor form and a nonlinear static sector type
controller is considered. A criterion of absolute strong asymptotic stability of
the null equilibrium is obtained using a quadratic form Lyapunov functional.
The construction of such a functional is reduced to solving a Lur'e system of
equations. A sufficient strict circle criterion of solvability of the latter is found,
which is based on...
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