Vijay V. Patel

H ∞ -based synthesis for a robust controller of interval plants

The synthesis of a robust controller for a SISO interval plant is carried out by converting the numerator and denominator parametric uncertainty to an uncertainty band around the numerator and denominator polynomials of the nominal plant model and then applying the standard H∞ method for the mixed sensitivity problem in which the selection of weighing functions is made using Kharitonovs polynomials.

Solution to the “Champagne problem” on the simultaneous stabilisation of three plants

Abstract In this paper, the problem proposed in Blondel et al. (SIAM J. Optim. 32 (2) 572–590) as an illustration of the difficulty of the simultaneous stabilization problem has been solved. The same problem was also mentioned in Blondel and Gevers (Math. Control, Signals, Systems 6 (1994) 135–145), where a bottle of good French champagne was offered for its solution. A new open problem is proposed based on the solution of the problem in this paper.

Classification of units in H/sub /spl infin// and an alternative proof Kharitonov's theorem

The authors present an alternative proof of Kharitonovs theorem, using the property of a ratio of odd and even parts of a Hurwitz polynomial and the Nyquist stability criterion. The ratio of Kharitonovs polynomials in the classification of units in H/sub /spl infin//, along with its relation to the problem of simultaneous stabilization of one parameter family of plants is discussed. A new theorem on the existence of a Hurwitz polynomial such that its ratio with a Hurwitz interval polynomial family with either the same even or odd part, is a strictly positive real (SPR) function is proved. It is also proved that if the ratio of a polynomial /spl beta/(s) with four Kharitonovs polynomials is an SPR function, then the ratio of /spl beta/(s) with the interval family is an SPR function.

A modification of theorem for the least bound of the minimum degree of interpolating unit

Abstract Theorem 1 for the least bound on the degree of interpolating unit in [1] requires to check both positive definiteness and negative definiteness of the Nevanlinna-Pick matrix.

A counter example for the conjecture in “an algorithm for interpolation with units in H ∞

Abstract It is conjectured by Dorato et al. [Automatica,25, 427–430 (1989)], that the algorithm given by them for interpolation with units in H∞, gives the lowest possible degree unit. A counter example presented in this technical communication shows that this is not the case for real as well as complex interpolation data.

Comments on "On Hurwitz stable polynomials and strictly positive real transfer functions"

The above paper [see ibid., vol. 48, p. 127-8, 2001] comments on the original paper [see ibid., vol. 44, p. 454-8, 1997]. However, the authors do not agree with the abstract of the above paper. The main reasons for this are given.

H∞-Robust Optimal Controller with Integral Action for a Coupled Tank System

The design of an H∞-optimal controller incorporating integral action via polynomial approach for a coupled tank system and a PC based implementation are described. The suboptimal H∞-controller obtained via state space method is reduced to an optimal controller with the insight obtained from the polynomial approach. The choice of the weighting functions for H∞—optimal controller, advantages and limitations of state space and polynomial techniques are discussed in full detail.

On least-degree unit interpolation in RH∞

Examples are presented that give insight and suggest why it is difficult to develop a unit interpolation algorithm that will yield an interpolating unit in RH∞ of least degree.