convergence and stability of distributed stochastic iterative processes a mathematical framework is proposed for convergence analysis of stochastic iterative processes arising in applications of pseudogradient optimization algorithms the framework is based upon the concepts of stochastic difference inequalities and vector lyapunov functions which are ideally suited for reducing the dimensionality problem arising in testing convergence of distributed parallel schemes by applying the m matrix conditions to a test matrix having a dimension equal to the number of the processor in the scheme one can use the framework to select suitable scaling factors for each individual processor producing a satisfactory convergence rate of the overall iterative process the results provide new convergence tests for distributed iterative processes arising in decentralized extremal regulation adaptation and parameter estimation schemes

a two dimensional adaptive pseudo spectral method we develop a two dimensional adaptive pseudo spectral procedure which is capable of improving the approximation of functions which are rapidly varying in two dimensions the method is based on introducing two dimensional coordinate transformations chosen to minimize certain functionals of the solution to be approximated the method is illustrated by numerical computation of the solutions to a system of reaction diffusion equations modeling the gasless combustion of a solid fuel spatio temporal patterns are computed as a parameter related to the activation energy is increased above a critical value c the spatial patterns are characterized by a very rapid variation in the direction of the axis of the cylinder together with a standing wave pattern in the direction of the azimuthal angle for small values of c the solutions exhibit a nearly sinusoidal dependence in both time and as is increased further relaxation oscillations in both time and occur beyond a critical value of stable time periodic solutions are no longer found and the solution exhibits a quasi periodic time dependence

essentially nonoscillatory spectral fourier methods for shock wave calculations in this paper we present an essentially nonoscillatory spectral fourier method for the solution of hyperbolic partial differential equations the method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the fourier method the high accuracy away from the shock is enhanced by using filters numerical results confirm that essentially no oscillations develop in the solution also the accuracy of the spectral solution of the inviscid burgers equation is shown to be higher than a fixed order

contractibility of dynamic lti controllers using complementary matrices a generalized structure of complementary matrices involved in the input state output inclusion principle for linear time invariant systems including contractibility conditions for static state feedback controllers is well known in this note it is shown how to further extend this structure when considering contractibility of dynamic controllers necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion contraction transformation matrices explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion contraction transformation matrices moreover these conditions are further specialized for a particular class of transformation matrices

generalized selection of complementary matrices in the inclusion principle this paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state lq optimal control of lti systems it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design

brief paper controllability and observability of expanded systems with overlapping decompositions the expanded system concept of siljak and his coworkers enables the design of robust overlapping controllers and observers for large scale systems to be carried out in a purely decentralised way in this paper we study the stability and detectability properties of expanded systems and show that it is only in certain special cases that these properties are preserved when the system is expanded these special cases define the classes of systems where the expanded system concept can be used for controller or observer design

overlapping block diagonal dominance and existence of liapunov functions the main objective of this paper is to formulate a generalization of block diagonal dominance which can be used to establish nonsingularity of matrices via overlapping diagonal blocks a number of stability results are derived in the new setting by exploiting the well known m matrix properties as well as extensions of the normalization scaling and alternative norm utilization a link between generalized block diagonal dominance and vector liapunov functions is established which can be applied in the stability analysis of interconnected dynamic systems

brief paper on the v stability of complex dynamical networks this paper introduces the concept of lyapunov v stability for complex dynamical networks under the new framework each dynamical node is associated with a passivity degree which indicates to what extent an effort is required for stabilizing the node from this approach the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network pinning control is then suggested and investigated based on the new v stability formulation as an illustrative example a network with different node dynamics and non uniform coupling strengths is simulated to verify the analytic results moreover a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed v stability criterion and stabilization scheme

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

bounded minimum distance decoding of unit memory codes we propose an algorithm for bounded minimum distance decoding of partial unit memory codes up to half the designed extended row distance it makes use of a reduced trellis with the nodes found by bounded minimum distance decoding of the block codes used in the unit memory code the results can be extended to general multimemory codes the complexity of this algorithm is upper bounded by 2 d sub 1sup r 2d sub spl alpha times the complexity of the bounded minimum distance decoder of the block codes in the unit memory code here d sub spl alpha is the linear increase of the designed extended row distance d sub isup r

global properties of pseudospectral methods abstract we apply polynomial interpolation methods both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations the derivative matrix for a general sequence of collocation points is explicitly constructed we explore the effect of several factors on the performance of these methods we show that global methods cannot be interpreted in terms of local methods for example the accuracy of the approximation differs when large gradients of the function occur near the center of the region or in the vicinity of the boundary this difference does not depend on the density of the collocation points near the boundaries hence intuition based on finite difference methods can lead to false results

generalized decompositions of dynamic systems and vector lyapunov functions the notion of decomposition is generalized to provide more freedom in constructing vector lyapunov functions for stability analysis of nonlinear dynamic systems a generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state space of a given system an inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system so that stabliity of the expansion implies stability of the original system stability of the expansion can then be established by standard disjoint decompositions and vector lyapunov functions the applicability of the new approach is demonstrated using the lotka voiterra equations

mappings and accuracy for chebyshev pseudo spectral approximations abstract the effect of mappings on the approximation by chebyshev collocation of functions which exhibit localized regions of rapid variation is studied a general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials a particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications it is shown that the mapped function can be approximated much more accurately by chebyshev polynomial approximations than the original function the effect on the approximation of introducing subdomains is also studied the accuracy of the pseudo spectral approximation is very sensitive to the location of the interface although this sensitivity is reduced when mappings are employed within the subdomains

partial exponential stability of semi state systems the general class of non linear non autonomous semi state systems is considered from the viewpoint of stability of system motions a theorem is proved giving necessary and sufficient conditions for partial exponential stability of arbitrary motion of these systems over finite or infinite time intervals the results are illustrated by the analysis of a non linear electrical circuit

a decomposition technique for nonlinear dynamical system analysis a method for analyzing large scale nonlinear dynamical systems by decomposing them into coupled lower order subsystems that are sufficiently simple for computational analysis is presented it is shown that the decomposition approach can be used to scale the sum of squares programming framework for nonlinear systems analysis the method constructs subsystem lyapunov functions which are used to form a composite lyapunov function for the whole system further computational savings are achieved if a method based on sparsity maximization is used to obtain the subsystem lyapunov functions

the majorant lyapunov equation a nonnegative matrix equation for robust stability and performance of large scale systems a new robust stability and performance analysis technique is developed the approach involves replacing the state covariance by its block norm matrix i e the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics a bound i e majorant for the block norm matrix is given by the majorant lyapunov equation a lyapunov type nonnegative matrix equation existence uniqueness and computational tractability of solutions to the majorant lyapunov equation are shown to be completely characterized in terms of m matrices two examples are considered for a damped simple harmonic oscillator with uncertain but constant natural frequency the majorant lyapunov equation predicts unconditional stability and for a pair of nominally uncoupled oscillators with uncertain coupling the majorant lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators a result not predictable from quadratic or vector lyapunov functions

an inclusion principle for hereditary systems abstract given two hereditary dynamic systems having different dimensions the conditions are provided under which a part of the motion of the larger system is reproduced by the smaller system that is the larger system includes the smaller one the conditions for inclusion are useful in applying the concept of vector liapunov functions to stability analysis of systems composed of overlapping subsystems by expanding the systems into a larger space the overlapping subsystems appear as disjoint and standard methods can be used to conclude stability of the expanded system under the inclusion conditions stability of the expansion implies stability of the original system an example is provided to show stability where the standard disjoint decompositions fail

nested e decompositions and clustering of complex systems abstract a graph theoretic method of extreme simplicity is proposed for decomposition and clustering of complex systems into interconnected subsystems with prescribed interaction strength the method is suitable for stability analysis via vector lyapunov functions and decentralized control and estimation of large scale systems the new decomposition scheme can be used in clustering aggregation of models in economics queuing networks and computer systems as well as decompositions in block iterative methods for solutions of linear algebraic equations

hierarchical liapunov functions abstract a complex system is considered as a collection of dynamic components which may be combined in different ways to form stable subassemblies subsystems which may serve again as units to build still more complex stable configurations a hierarchical liapunov function is proposed which can be used to determine stability of the overall system obtained by the multilevel interconnection process stability when established in this way is hierarchically connective that is if at any instant in time the hierarchical evolution of the system is interrupted the system can fall apart in exactly the same way it was constructed and by re starting the process put together again without loss of stability this fact may be used to explain the evolution of stable forms in natural as well as man made systems

an adaptive pseudo spectral method for reaction diffusion problems the spectral interpolation error was considered for both the chebyshev pseudo spectral and galerkin approximations a family of functionals i sub r u with the property that the maximum norm of the error is bounded by i sub r u j sub r where r is an integer and j is the degree of the polynomial approximation was developed these functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize i sub r u the number of collocation points is then chosen to maintain a prescribed error bound the method is illustrated by various examples from combustion problems in one and two dimensions