Abstract
Abstract Hassan and Amin (1987) and Amin and Hassan (1987) have presented a simple algebraic solution for the ‘time-optimal output deadbeat’ (TOOD) regulator problem. This solution, which consists of a state feedback control law, has been obtained for right-invertible systems. These results are generalized here to accom- modate all classes of output-controllable left-invertible systems S(A, B, C, E). The design of TOOD regulators with internal stability for all classes of right- or output- controllable left-invertible systems S(A, B, C, E) is also considered. It is shown that the right Wiener-Hopf factorization at infinity of H(z)—the transfer function matrix of S—is the key tool for solving all TOOD regulator problems. Moreover, the internal stability problem, which will arise if any invariant zero of S is unstable, is solved by designing a TOOD regulator with internal stability. Finally, numerical examples are worked out to illustrate the generality of the proposed method.
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