Kanti B. Datta

Orthogonal functions in systems and control

Orthogonal functions in systems and control - a historical perspective least squares approximation of signals signal processing in continuous-time domain analysis of time-delay systems identification of lumped parameter systems identification of linear time-invariant distributed parameter systems identification of linear time-varying and nonlinear distributed parameter systems optimal control of linear systems.

H2/H∞ Control of discrete singularly perturbed systems

The design of a mixed H2/H∞ linear state variable feedback suboptimal controller for a discrete-time singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index both are O(e) close to those synthesized using the full order system.

Identification via Fourier series for a class of lumped and distributed parameter systems

The operational matrix of integration and a one-shot operational matrix for repeated integration (OSOMRI) are used to estimate the parameters and the initial and boundary conditions of linear, time-invariant, lumped-parameter systems. It is demonstrated that OSOMRI provides better accuracy than the conventional operational matrix of integration. An algorithm for distributed-parameter system identification using Fourier series is included. A comparative study of the estimates obtained by the proposed method for both types of system with those in the literature obtained by other methods is carried out. >

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.

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.

Linear time-invariant distributed parameter system identification via orthogonal functions

Abstract This paper points out the mathematical inconsistencies traced in the literature on the identification problem of linear time-invariant distributed parameter systems via orthogonal functions, and proposes for the same problem a unified identification approach based on the concept of one shot operational matrix for repeated integration. It presents identifiability requirements for the block-pulse functions approach while suggesting a linear independence test for the full column rank of linear algebraic system arising out of the system model upon the application of orthogonal functions. Finally, it illustrates system identification with a numerical example.

Analysis of time-delay systems via shifted Chebyshev polynomials of the first and second kinds

A novel and general approach for obtaining the delay operational matrix of shifted Chebyshev polynomials of first or second kind is presented. This operational matrix is exact in the sense that it does not involve any approximation. Next, this paper shows the application of the delay operational matrix in the analysis of time-delay systems. Two illustrative examples are included and the results are compared with those obtained by the exact method.

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.

Analysis of linear time-invariant time-delay systems via orthogonal functions

This paper first critically reviews the up-to-date literature available on the problem of analysis of linear time-invariant dynamical systems containing time delay(s) and discusses the practical limitations and shortcomings of existing orthogonal functions techniques. Then it presents some mathematical preliminaries very important for the analysis of delay systems. As a part of this, it introduces: the derivative operational matrix of Legendre, Laguerre, Hermite and Fourier orthogonal systems; the delay-integration operational matrix of orthogonal polynomial systems; a new integration operational matrix of Fourier orthogonal system; and the error analysis of arbitrary function in terms of these orthogonal functions and some approximate tools. Next, it proposes delay operational matrix approach and time-partition technique for the analysis of delay systems. It shows that recursive algorithms are possible if block pulse functions are used in the proposed methods whose practical limitations are also pointed ...

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.