Robust stability of linear quadratic state feedback regulator under system uncertainty

Katayama, Tohru; Sasaki, Seiji

doi:10.1080/00207178708933739

Cited by 5 publications

(7 citation statements)

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“…For the above class of systems, the method of Katayama and Sasaki (1987) can be used to select weighting matrices a and R in the cost function I Joo…”

Section: Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Recently, several researches (Katayama and Sasaki 1987, Tsay et al 1991) show that the LQ regulators are robust with respect to large parameter perturbations in the system and input matrices, provided the perturbations satisfy or nearly satisfy the 'matching conditions' (Leitmann 1979). In particular, for a class of uncertain systems with linear nominal dynamics and nonlinear perturbations, Katayama and Sasaki (1987) give explicit relations between bounds of peturbations and the weighting matrices in the performance index so that stabilizing state feedback gains can be obtained.In many practical applications, however, the system states are not directly available for feedback. A number of approaches (Petersen 1985, Steinberg and Corless 1985, Galimidi and Barmish 1986, Walcott and Zak 1988 for synthesizing robust observers or output feedback have been developed.…”

mentioning

confidence: 99%

“…In this paper, we propose another method for handling such cases. We show that the robust LQ state feedback controller developed by Katayama and Sasaki (1987) can be used in the observer-based configurations with full-or reduced-order observer to asymptotically stabilize the nonlinear uncertain system satisfying the matching conditions. Thus the LQ controller can be designed first without considering the availability of the states, and a robust observer is then designed to provide the necessary state information.…”

mentioning

confidence: 99%

“…In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Robust observer design for nonlinear uncertain systems with LQ regulators

Fong

Tsay

Kuo

1992

International Journal of Systems Science

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For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987)that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers. IntroductionIn the past two decades, the LQ technique for designing optimal state feedback controllers has received considerable interest (Anderson and Moore 1971, Safonov andAthans 1977). Recently, several researches (Katayama and Sasaki 1987, Tsay et al. 1991) show that the LQ regulators are robust with respect to large parameter perturbations in the system and input matrices, provided the perturbations satisfy or nearly satisfy the 'matching conditions' (Leitmann 1979). In particular, for a class of uncertain systems with linear nominal dynamics and nonlinear perturbations, Katayama and Sasaki (1987) give explicit relations between bounds of peturbations and the weighting matrices in the performance index so that stabilizing state feedback gains can be obtained.In many practical applications, however, the system states are not directly available for feedback. A number of approaches (Petersen 1985, Steinberg and Corless 1985, Galimidi and Barmish 1986, Walcott and Zak 1988 for synthesizing robust observers or output feedback have been developed. In this paper, we propose another method for handling such cases. We show that the robust LQ state feedback controller developed by Katayama and Sasaki (1987) can be used in the observer-based configurations with full-or reduced-order observer to asymptotically stabilize the nonlinear uncertain system satisfying the matching conditions. Thus the LQ controller can be designed first without considering the availability of the states, and a robust observer is then designed to provide the necessary state information. For the full-order observer-based control configuration, we develop an algorithm for computing the robust observer gain matrix of the Luenberger obser-

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“…For the above class of systems, the method of Katayama and Sasaki (1987) can be used to select weighting matrices a and R in the cost function I Joo…”

Section: Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%