Ezra Zeheb

Stability independent and dependent of delay for delay differential systems

Abstract We provide new proofs to modified equivalent conditions for stability independent of delay of retarded and neutral delay differential systems. We also present a new test procedure for stability independent of delay. If the system is not stable independent of delay, the test is further applicable to obtain the intervals of delay for which the system is asymptotically stable. The usefulness and simplicity of the new test procedure is illustrated by numerical examples.

On Routh-Pade model reduction of interval systems

This paper discusses another generalization of the direct Routh table truncation method for interval systems. It is shown that the existing generalization of the direct Routh table truncation fails to produce a stable system, in contradiction to the equivalent result for fixed-coefficients systems. The present method guarantees a stable reduced order model for interval systems as well.

N-dimensional stability margins computation and a variable transformation

Stability margins for N-dimensional ( N \geq 2 ) linear discrete causal systems are defined, following a definition suggested recently in the literature for N = 2. These can serve as a measure, in some sense, for the tendency of a stable N-D system to become unstable. Also presented is a new procedure for the computation of these stability margins, which is explicitly formulated. The computational complexity is equivalent to that of solving for one indeterminate a set of N + 1 real equations in N + 1 real indeterminates. Also, an N-dimensional expansion of a known variable transformation which preserves the core condition of stability is presented and used to considerably simplify N-dimensional stability tests and stability margins computations for a class of special cases. Numerical examples are also provided.

Design of robust strictly positive real transfer functions

Sufficient conditions are derived for the existence of a fixed coefficients polynomial c*(s) such that (c*(s))/(a(s)) is a strictly positive real (SPR) transfer function, where a(s) belongs to the set of interval stable polynomials. The design procedure is described, when these conditions are satisfied, using an illustrative example. >

Design of a Robust State Feedback Controller for a STATCOM Using a Zero Set Concept

A static synchronous compensator (STATCOM) is one of the fundamental flexible ac transmission system devices that can be used for voltage regulation and dynamic voltage control. In this paper, a new approach to the problem of the STATCOM state feedback design is presented. The proposed solution technique is based on a zero set concept. It allows one to calculate a complete set of the admissible feedback gains that place closed-loop poles into a prespecified region in the complex plane under parametric uncertainties in the plant model. These uncertainties represent load pattern variations and topological changes due to line tripping. Computational examples show that by using the design technique based on the zero set concept, it is possible to derive the state feedback controllers with better robustness properties than those achieved using the approaches utilizing linear matrix inequalities.

Frequency response envelopes of a family of uncertain continuous-time systems

Amplitude and phase envelopes of a family of interval rational transfer functions of continuous-time systems are derived. A finite number of intervals on the real frequency axis are explicitly determined, for which the maximum and the minimum amplitude or phase of the functions, with respect to the interval coefficients, coincide with explicit fixed coefficients functions. Some special cases where simplifications are applicable, are pointed out. Illustrative examples that are consistent with the derived results are provided. >

Sign test of multivariable real polynomials

New theorems and procedures are presented for testing positivity and nonnegativity of a real polynomial in n real variables. The methods pertain to global as well as nonglobal or local sign tests for any closed intervals of the variables. A dimension growth is not required, and the methods depend on resolution of the solution of a set of n equations in n variables. Also provided is a simplified estimation of the computational effort involved in the present procedures, as compared to procedures where a dimension growth is required. Several illustrative examples are also provided.

A Note on Spectral Conditions for Positive Realness of Transfer Function Matrices

Necessary and sufficient conditions for positive realness of general transfer function matrices are derived. The conditions are expressed in terms of eigenvalues of matrix functions of the state matrices representation of the LTI system. Illustrative numerical examples are provided.

Reduced order IIR approximation to FIR digital filters

An algorithm for designing an infinite-impulse-response (IIR) stable filter using a finite-impulse-response (FIR) given filter, with the objective of reducing the delay and order, is described. The design is in the time domain using the least-squares-inverse algorithm, which is briefly described. In this method, the numerator of the approximated filter is part of the FIR filter itself and no calculations and minimization are needed to find the numerator coefficients (except finding the FIR roots). An error analysis between the given FIR and approximated IIR filters is provided. This error analysis enables the designer to fix a design parameter, often unnoted, keeping the energies of the approximated and original filters equal. Results and two illustrative examples are presented. >

On the largest modulus of polynomial zeros

A result by Cauchy (1829) is extended in two directions, providing two bounds for the moduli of the zeros of a polynomial. One of these pertains to real polynomials, and the other pertains to polynomials with complex coefficients. >