Equivalent State-space Realization Research Articles

An efficient hybrid estimator for nonlinear channels in state space

This paper presents a method for estimation of nonlinear communication channels using Gaussian wavelet estimator (GWE). Results obtained using this approach is compared with image enhanced interacting multiple model (IMM-IE) extracted from the literature. Comparison reveals that the IMM-IE and the GWE require the same number of Kalman filters, but the GWE extrapolates more initial conditions. If the performance of the two algorithms is equivalent, the IMM-IE is less complex, but GWE is technically efficient. Here, we have presented the state-space approach instead of the transfer function approach, as the state-space approach can be easily extended to nonlinear mixing systems. Moreover, the state-space approach not only gives an efficient internal description of the dynamic systems, but there also exist different possible equivalent state-space realizations.

An Efficient State-Space Realization With Minimum Roundoff Noise Gain

This paper deals with efficient digital filter structures with roundoff noise consideration. Motivated by the direct-form II transposed (DFIIt) structure in rho-operator (rhoDFIIt) an alternative structure is obtained [Li in 2005, where, instead of the first-order rho-operators in rhoDFIIt, a set of second-order polynomial operators is used. In this paper, with the rounding before multiplication implementation taken into account, the equivalent state-space realization of the proposed structure by Li is derived and its roundoff noise performance is analyzed by deriving the roundoff noise expressions without/with error feedback consideration. This state-space realization can be efficiently implemented and has more degrees of freedom than its counterpart rhoDFIIt, which can be utilized to minimize the roundoff noise gain. A genetic algorithm is proposed to efficiently solve the optimal structure problem. Extensive examples are given to illustrate the advantage of this state-space realization and support the theoretical analysis

On the Generalized DFIIt Structure and its State–Space Realization in Digital Filter Implementation

It is well known that for a digital filter of order p, the number of nontrivial parameters in the classical optimal state-space realizations is proportional to p/sup 2/, while the traditional shift operator z-based direct-form II transposed (zDFIIt) structure, though having poor numerical properties, is one of the most efficient structures, just possessing 3p+1 nontrivial parameters. In this paper, based on the concept of polynomial operators, a new structure is proposed for digital filter implementation, which is a generalization of the traditional zDFIIt and the prevailing /spl delta/DFIIt structures. This structure, denoted as /spl rho/DFIIt, possesses 3p+1 nontrivial parameters plus p parameters at choice. Expressions for evaluating the sensitivity measure and the roundoff noise gain are derived for the /spl rho/DFIIt structure and its equivalent state-space realization that has the same structure complexity. It is shown that the state-space realization always yields a smaller roundoff noise gain than the /spl rho/DFIIt structure. One of the nice properties of these two structures is that for a given digital filter, they can be optimized with the p free parameters. The optimal structure problems can be solved with exhaustive researching under practical considerations. Numerical examples are presented to illustrate the design procedure.

A Perspective on Singularity in 2D Linear Systems

In modelling physical systems it frequency turns out that only the so-called singular (also termed descriptor or implicit in the literature) form of the state equations can be obtained. Then the derivative of the state vector for the continuous case or the next value of the state vector for the discrete case is pre-multiplied by a square singular (or even rectangular) matrix. Such models have more complex structure than their standard (also termed non-singular in the literature) counterparts with subsequent implications in terms of, for example, controller design. Note, however, that singularity is also useful, e.g. it can be used to derive the so-called semi-state description in cases when it is impossible to derive the state space description. In some cases, however, singularity is not an intrinsic feature of the system but is due, for example, to the effects of ‘non-adequate’ modelling or the method employed to construct the model. For a given example of this last case, a standard model may exist but is very difficult to construct. One way of avoiding singularity is to apply (if possible) well established algebraic transformations to the state vector. In this paper, an overview of recent results on singularity of equivalent state space realizations of 2D linear systems and methods for avoiding this property is given. For example, the role of inversion and bilinear transformations in the latter respect are treated together with singularity of the so-called linear repetitive processes and the introduction of this property as the result of discretization.

State-space realizations of MIMO 2D discrete linear systems Elementary operation and variable inversion approach

Elementary operations are an alternative to the polynomial system matrix for studying basic systems theoretic properties of standard (1D) linear systems, such as state-space realizations. In the general area of nD systems, there is a basic need to analyse both rational and polynomial matrices in n indeterminates. This paper develops key results on using elementary operations and variable inversions to produce equivalent state-space realizations of MIMO 2D systems.

Control of Nonlinear Differential-Algebraic-Equation Systems with Disturbances

We address the control of a class of nonlinear, multivariable, high-index differential-algebraic-equation systems with external disturbances. Initially, an algorithmic procedure is developed to derive an equivalent state-space realization of the constrained system, valid for arbitrary disturbances. Then, on the basis of the derived state-space realization, a feedforward/feedback controller is developed to completely eliminate the effects of the measurable disturbances and induce a well-characterized input/output behavior in the constrained system. The application of the proposed control methodology is illustrated on a high-purity absorption column.