phase margins for multivariable control systems this paper presents a new definition for the phase margin of multivariable systems the properties of the phase margin are such that a stable closed loop multi input multi output system will remain stable for all unitary perturbations in the feedback path whose phases are less than the phase margin of the system it is also shown that the definition of phase margin is invariant under unitary transformations of the system

comments on stability margin evaluation for uncertain linear systems the bound derived in the above paper by gong thompson ibid vol 39 no 3 p 548 50 1994 is shown via two new stability criteria not to be the tightest possible for all unstructured perturbations a minor error of their theorem is also corrected

detection estimation of very close emitters performance breakdown ambiguity and general statistical analysis of maximum likelihood estimation we reexamine the well known problem of threshold behavior or performance breakdown in the detection estimation of very closely spaced emitters in this extreme regime we analyze the performance for maximum likelihood estimation mle of directions of arrival doa for two close gaussian sources over the range of sample volumes and signal to noise ratios snrs where the correct number of sources is reliably estimated by information theoretic criteria itc but where one of the doa estimates is severely erroneous outlier we show that random matrix theory rmt applied to the evaluation of theoretical mle performance gives a relatively simple and accurate analytical description of the threshold behavior of mle and itc in particular the introduced single cluster criterion provides accurate ambiguity bounds for the outliers

a block pulse operational matrix method for solving two dimensional nonlinear integro differential equations of fractional order abstract in this paper we use two dimensional block pulse functions 2d bpfs and their operational matrix for integration and fractional integration to reduce two dimensional fractional integro differential equations 2d fides to a system of nonlinear algebraic equations the solution is determined by solving this system also by two theorems we prove the convergence of the proposed method finally the numerical solutions guarantee the desired accuracy and efficiency

fractional order integral equations of two independent variables in this paper we present some results concerning the existence the uniqueness and the attractivity of solutions for some functional integral equations of riemann liouville fractional order by using some fixed point theorems

a generalization of strong kharitonov theorems to polytopes of polynomials the root clustering property of a certain class of polytopes of polynomials is examined it is shown that the polytopes of polynomials have only zeros within the left sector if and only if a subset of their edge polynomials has only zeros within the left sector certain conditions are derived under which the root clustering property of the polytopes of polynomials can be inferred from a subset of their vertices

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

threshold performance analysis of maximum likelihood doa estimation the purpose of this paper is to investigate the nonasymptotic behavior of the maximum likelihood method in the context of lacunar array processing we derive an analytical expression of the maximum likelihood mean square error which is now valid for all signal to noise ratio snr ranges we also provide an analysis of the snr threshold phenomena which allows us to derive closed form formulas for the threshold values computer simulations confirm the validity of the theoretical investigations

a dual result to kharitonov s theorem a dual problem to kharitonov s problem involving a diamond instead of a rectangle is considered the results show that a family of polynomials with coefficients varying in the diamond is strictly hurwitz if and only if eight one dimensional exposed edges of the diamond are strictly hurwitz

on the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices this paper analyzes the asymptotic behavior of the sample estimators of the eigenvalues and eigenvectors of covariance matrices rather than considering traditional large sample size asymptotics in this paper the focus is on limited sample size situations whereby the number of available observations is comparable in magnitude to the observation dimension using tools from random matrix theory the asymptotic behavior of the traditional sample estimates is investigated under the assumption that both the sample size and the observation dimension tend to infinity while their quotient converges to a positive quantity assuming that an asymptotic eigenvalue splitting condition is fulfilled closed form asymptotic expressions of these estimators are derived proving inconsistency of the traditional sample estimators in these asymptotic conditions the derived expressions are shown to provide a valuable insight into the behavior of the sample estimators in the small sample size regime

numerical methods for solving two dimensional nonlinear integral equations of fractional order by using two dimensional block pulse operational matrix in this paper our purpose is to construct a two dimensional fractional integral operational matrix and its use for the numerical solution of two dimensional fractional integral equations we use these operational matrices and properties of two dimensional block pulse functions 2d bpfs to reduce two dimensional fractional integral equations 2d fies to a system of algebraic equations obtained algebraic system based on the original problem can be linear or nonlinear then we show convergence of the proposed methods and we find the error bounds to show the accuracy efficiency and speed of the proposed method linear and nonlinear examples are presented

robustness analysis for linear dynamical systems with linearly correlated parametric uncertainties the authors propose an approach for robust pole location analysis of linear dynamical systems with parametric uncertainties linear control systems with characteristic polynomials whose coefficients are affine in a vector of uncertain physical parameters are considered a design region in complex plane for system pole placement and a nominal parameter vector generating a characteristic polynomial with roots in that region are given the proposed method allows the computation of maximal domains bounded by linear inequalities and centered at the nominal point in system parameter space preserving system poles in the given region the solution of this problem is shown to also solve the problem of testing robot location of a given polytope of polynomials in parameter space it is proved that for stability problems for continuous time systems with independent perturbations on polynomial coefficients this method generates the four extreme kharitonov polynomials

numerical solution of nonlinear volterra fredholm integro differential equations via direct method using triangular functions an effective direct method to determine the numerical solution of the specific nonlinear volterra fredholm integro differential equations is proposed the method is based on new vector forms for representation of triangular functions and its operational matrix this approach needs no integration so all calculations can be easily implemented some numerical examples are provided to illustrate the accuracy and computational efficiency of the method

a first order lyapunov robustness method for linear systems with uncertain parameters a method for stability robustness analysis based on a quadratic lyapunov function that varies linearly with uncertainty parameters is derived linear time invariant systems with structured uncertainties are discussed the lyapunov function is optimized numerically to maximize the robustness region in parameter space numerical results are given for four examples in which the first order method is compared to previous lyapunov methods for robustness analysis while the zero order method is slightly better than the first order method for one example the first order method is clearly superior in the other three more realistic examples the first order method is especially superior for applications to active control of flexible structures where robustness with respect to unmodeled coupling between modeled modes are important issues for such applications the first order method is much better at detecting the increased robustness associated with increased separation between frequencies

an implicit numerical method for the two dimensional fractional percolation equation in this paper an implicit numerical method for the two dimensional fractional percolation equation without the assumption of continued and rigid body motion is proposed consistency stability and convergence of the implicit finite difference method are established finally some numerical examples are given the numerical results demonstrate the effectiveness of the theoretical analysis

stability margin evaluation for uncertain linear systems a sufficient stability condition for parameter variation in a perturbed continuous time multivariable linear system represented by a state space model is presented starting with the existence of an algebraic riccati equation a stability bound is derived from the polar decomposition of the nominal system matrix unlike previous work the results are not dependent on the solution of the lyapunov equation and consequently not a function of an arbitrarily selected positive definite matrix in addition the bound would appear to be the tightest possible in that violation of the presented inequality can be shown to lead to instability

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

numerical solution of nonlinear volterra fredholm integro differential equations the aim of this paper is to present an efficient analytical and numerical procedure for solving the high order nonlinear volterra fredholm integro differential equations our method depends mainly on a taylor expansion approach this method transforms the integro differential equation and the given conditions into the matrix equation the reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments

numerical solution of fractional differential equations using the generalized block pulse operational matrix the riemann liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration also the generalized block pulse operational matrices of differentiation are derived based on the above results we propose a way to solve the fractional differential equations the method is computationally attractive and applications are demonstrated through illustrative examples

a counterexample of comments on stability margin evaluation for uncertain linear systems in the original paper c gong and s thompson ibid vol 39 p 548 50 1994 there is given what is claimed to be the tightest bound for all unstructured pertubations such that a specified system keeps its asymptotic stability j h su ibid vol 39 p 2523 4 1994 showed that it is not the tightest bound and gives another bound that bound is shown by a counterexample to be incorrect