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Multiple loop linear time invariant feedback systems stability, discussing conditions, gain matrix and input-output properties

Optimal characteristics for single-input single- output memoryless time invariant nonlinear dynamic systems

If all eigenvalues of all matrices Ai (i=0, 1, 2, ...) lie in a disc of radius

Re represents a linear time-invariant system of order n + h. When e → 0, Re, reduces to R0 of order n ≤ n + h. Conditions are given under which the bounded-input bounded-state stability of R0 implies that of Re and we show that, under these conditions, as e → 0, the state trajectories of Re approach those of R0 for any continuous input.