Disturbance tolerance and rejection of linear systems with imprecise knowledge of actuator input output characteristics

We study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics. Disturbances either bounded in energy or bounded in magnitude are considered. The actuator input output characteristics are assumed to reside in a so-called generalized sector bounded by piecewise linear curves. Robust bounded state stability of the closed-loop system is first defined and characterized in terms of linear matrix inequalities (LMIs). Based on this characterization, the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed-loop system under a given feedback law is formulated into and solved as optimization problems with LMI constraints.     

The gray-code filter kernels

In this paper, we introduce a family of filter kernels, the gray-code kernels (GCK) and demonstrate their use in image analysis. Filtering an image with a sequence of gray-code kernels is highly efficient and requires only two operations per pixel for each filter kernel, independent of the size or dimension of the kernel. We show that the family of kernels is large and includes the Walsh-Hadamard kernels, among others. The GCK can be used to approximate any desired kernel and, as such forms, a complete representation. The efficiency of computation using a sequence of GCK filters can be exploited for various real-time applications, such as, pattern detection, feature extraction, texture analysis, texture synthesis, and more     

A non-recursive method for solving the general discrete-time riccati equations related to the H∞ control problem

In this paper we propose a nonrecursive method for solving the general discrete-time algebraic Riccati equation related to the H_∞ control problem (H_∞-DARE). We have achieved this by casting the problem of solving a given H_∞-DARE to the problem of solving an auxiliary continuous-time algebraic Riccati equation associated with the H_∞ control problem (H_∞-CARE) for which the well known nonrecursive methods of solving are available. The advantages of our approach are: it reduces the computation involved in the recursive algorithms while giving much more accurate solutions, and it readily provides the properties of the general H_∞-DARE.     

User impersonation in key certification schemes

In this note we exhibit some weaknesses in two key certification schemes. We show how a legitimate user can impersonate any other user in an ElGamal-based certification scheme, even if hashing is applied first. Furthermore, we show how anybody can impersonate users of the modular square root key certification scheme, if no hashing occurs before the certification. This shows that it is essential for this certification scheme to hash a message before signing it.     

On the characteristics of extreme values for series systems

This paper investigates the characteristics of extreme events for series systems. A methodology is developed to determine the Gumbel Type of a series system, given that the Gumbel Types of the components are known. Determining the propagation of the Gumbel Types can be accomplished without knowing the exact probability density functions of the components and without calculating the analytic form for the distribution of the overall system. In addition, an analytical technique is developed to determine the parameters of the extreme value distribution—the characteristic largest value, and the inverse measure of dispersion—for the overall series system. Finally, these three pieces of information—the Gumbel Type, the characteristic largest value, and the inverse measure of dispersion—are combined to calculate a conditional expected value of extreme events of the overall series system.     

Inverse of linear systems

An algorithm is given for computing the inverse of a linear time-invariant multivariable system. The algorithm, which is an extension of an existing algorithm, reduces the problem to that of inverting a polynomial matrix, and hence requires less computations. A more efficient test for determining whether a system is invertible is also given.     

Range estimation from random array phase measurements

Estimation of the location of a source of radiation from antenna-array phase measurements is considered. A least-squares technique for estimation is analysed for performance.     

Computing the minimal polynomial by using Koenig's theorem

An algorithm is given to determine the transfer function or minimal realisation of a finite-dimensional linear time-invariant system from its Markov parameters or time moments. The method makes a direct computation of the minimal polynomial by using Koenig's theorem.