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—We present an adaptive controller that requires limited model information for stabilization, command following, and disturbance rejection for mult-input multi-output minimum-phase discrete-time systems. Specifically, the controller requires knowledge of the open-loop system's relative degree as well as a bound on the first nonzero Markov parameter.… (More)
— This paper considers the robust stabilization of single-input single-output (SISO) linear shift-invariant discrete-time systems. A non-minimal state-space realization is used to transform the original SISO system into a higher order realization with full-state measurement without knowledge of the system parameters. Robust stabilization is achieved using a… (More)
results of . This note, therefore, unveils a link between polynomial hyperbolicity and stability. Finally, as pointed out in [3, Sec. 18.9], the applications of frequency response convexity in robust control have only been minimally explored. The explicit LMI formulation described in this note may motivate further research along these lines.… (More)
— This paper is the second part of a pair of papers, which together present a direct adaptive controller for discrete-time systems that are possibly nonminimum phase.
This paper presents a direct model reference adaptive controller for single-input/single-output discrete-time (and thus sampled-data) systems that are possibly nonminimum phase. The adaptive control algorithm requires knowledge of the nonminimum-phase zeros of the transfer function from the control to the output. This controller uses a retrospective… (More)
— In this paper we investigate the robustness of an extended version of retrospective cost adaptive control (RCAC), in which less modeling information is required than in prior versions of this method. RCAC is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling… (More)
I n the popular literature there is a certain fascination with the concept of zero –. While today the inconspicuous 0 is taken for granted, the situation was different in the distant past. For example, the Romans had no symbol for 0, a fact memorialized by the jump from 1 B.C. to 1 A.D., a convention instituted in 531 A.D. [4, p. 91]. In contrast, the… (More)
— We extend retrospective cost adaptive control (RCAC) to command following for uncertain Hammerstein systems. We assume that only one Markov parameter of the linear plant is known and that the input nonlinearity is monotonic but otherwise unknown. Auxiliary nonlinearities are used within RCAC to account for the effect of the input nonlinearity.
— We present a discrete-time adaptive control algorithm that is effective for multi-input, multi-output systems that are either minimum phase or nonminimum phase. The adaptive control algorithm requires limited model information , specifically, the first nonzero Markov parameter and the nonminimum-phase zeros of the transfer function from the control signal… (More)
— We present a direct model reference adaptive controller for discrete-time systems (and thus sampled-data systems) that are possibly nonminimum phase. The adaptive control algorithm requires knowledge of the nonminimum-phase zeros of the transfer function from the control to the tracking error. This paper and its companion paper (Part 2) together analyze… (More)