A stability bound for systems with periodic output feedback

The authors present a stability bound on additive perturbations in the plant state matrix for systems with piecewise-constant, periodic output feedback. The bound does not require the calculation of the matrix exponential, but instead uses the matrix measure as an upper limit on its norm. This limit and a special norm based on the closed-loop eigenvectors are used to show that if the stability bound is satisfied, all the eigenvalues of the closed-loop discrete-time state matrix have magnitude less than one. It is also shown that if the stability bound is satisfied for two extreme perturbations, then the system is stable for all of the intermediate perturbations. Use of the stability bound is demonstrated by a numerical example