Robust stabilizability for a class of transfer functions

Kimura, Hidenori

doi:10.1109/tac.1984.1103663

Cited by 273 publications

(37 citation statements)

References 15 publications

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“…The only synthesis type result for interval plants that we are aware of is the one in [3], where the parametric uncertainty in the plant is bounded using an H , ball of perturbations, and results from H , theory [4] are used to synthesize a stabilizing controller for the entire plant family. Such an approach is not satisfactory because of at least two reasons.…”

Section: Introductionmentioning

confidence: 99%

Design of P, PI and PID controllers for interval plants

Datta

Bhattackaryya

1998

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)

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This paper considers the problem of designing P, PI and PID controllers that stabilize an interval plant family. Using results from the area of parametric robust control, these stabilization problems for an interval plant are first reduced to the equivalent problems of stabilizing either certain vertex plants (corresponding to the Kharitonov vertices) or certain segment plants (corresponding to the one-parameter generalized Kharitonov segments). Thereafter, recent results on P, PI and PID stabilization are invoked to obtain a complete characterization of all stabilizing P, PI and PID controllers for an interval plant family. Theorem 2.1 (Kharitonov's Theorem) Every polynomial in the interval family F is Hurwitz iff the following fourKharitonov polynomials are Hurwitz: K * ( S ) =~o + 2 1 s $ y 2 s 2 $~3 s 3 + x 4~4 + 2 5 8 5 + y 6~6 $ ---K2(S) = 20 + y l s + y2s2 $-X 3 s 3 + 24s4 + y5s5 + y6s6 + ... K 3 ( S ) = Y 0 + 2 1 S + X 2 S 2 + Y 3 s 3 + y 4 5 4 $ 2 5 S 5 + 2 6 S 6 $ . ' . K4(s) = yo + y1s + z2s2 + z3s3 + y4s4 + y5s5 + 2 6 2 + ' . . . 0-7803-4530-4198 $10.00 0 1998 AACC

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Section: Introductionmentioning

confidence: 99%

Design of P, PI and PID controllers for interval plants

Datta

Bhattackaryya

1998

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)

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“…Since then, there has been a vast amount of literature published on this subject, and it would be beyond the scope of this paper to review it here. Some insight into the available literature can be obtained from the following publications and their references: Bode ( 1949, Newton et al ( 1957), Zames (1966and 1981, Rosenbrock (1970 and1974), Desoer and Vidyasagar (1975), and Kimura (1984).…”

Section: Introductionmentioning

confidence: 99%

Robust stabilization of non-linear systems

Hammer

1989

International Journal of Control

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“…One reason why Nevanlinna-type interpolation problems have been investigated is that they are connected with system-, circuit-and control-theoretic issues as interpolation with positive-real functions [16], model approximation [ 5 ] , electrical power transfer [7], robust stabilization [8], and model matching in the Ha-norm [31.…”

Section: Introductionmentioning

confidence: 99%