Generalized State Space Systems Research Articles

Using statistical linearization to optimize a class of semi-active on-off control in a general state space system

Using statistical linearization to optimize a class of semi-active on-off control in a general state space system

Zero-order hold discretization of general state space systems with input delay

Abstract Plethora of applications in physics and engineering are dealing with systems that are subject to input delays. Despite the scientific focus, previous research investigated only state space systems with input delays. Here, we investigate the discretization of generalized state space system with input delay by using the zero-order hold method. Firstly, the solution of a continuous time, generalized state space system with input delay is addressed. By applying the appropriate zero-order hold sampling method, we transform a continuous time linear system into the equivalent discrete time system, while the discrete time solution of the equivalent system is analytically presented. Finally, we use local error metric to estimate the difference between the continuous time and discrete time solutions.

Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations

To implement the balancing based model reduction of large-scale dynamical systems we need to compute the low-rank (controllability and observability) Gramian factors by solving Lyapunov equations. In recent time, Rational Krylov Subspace Method (RKSM) is considered as one of the efficient methods for solving the Lyapunov equations of large-scale sparse dynamical systems. The method is well established for solving the Lyapunov equations of the standard or generalized state space systems. In this paper, we develop algorithms for solving the Lyapunov equations for large-sparse structured descriptor system of index-1. The resulting algorithm is applied for the balancing based model reduction of large sparse power system model. Numerical results are presented to show the efficiency and capability of the proposed algorithm.

Explicit solution and stability of linear time-varying differential state space systems

Linear time-varying (LTV) systems naturally arise when one linearizes nonlinear systems about a trajectory. In contrast the linear time-invariant (LTI) cases which have been thoroughly understood in the analysis and synthesis technologies, many features of the LTV systems are still limited and not clear. This paper addresses the problems of solution and stability of a general unforced LTV differential state space system. Unlike most of the work based on the Lyapunov theory, numerical simulations, or specific constraint systems, the paper proposes the spectral decompositions of the LTV systems by employing extended eigenpairs and with simple mathematical derivation. The spectral decompositions reveal the mechanisms of inherent characterization in general LTV systems, rather than a particular class. Moreover, a novel set of auxiliary equations is developed for guiding and obtaining the extended eigenpairs of its system matrix which completely characterize the LTV systems. The solutions to perform the commutative systems and the second-order systems with companion form are straightforward. The proposed innovative thinking provides a novel guided way to analyze the LTV systems. These findings are easily extended to LTI cases. Examples from the literature demonstrate the effectiveness and the superiority of the proposed approaches when compared with other methods. The proposed results may be of great interest in both for scientific research and application.

Analytical study for singular system of transistor circuits

Abstract In this paper, we propose a user friendly algorithm based on homotopy analysis transform method for solving observer design in generalized state space or singular system of transistor circuits. The homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The effectiveness of technique is described and illustrated with an example. The obtained results are in a good agreement with the existing ones in open literature and it is shown that the scheme proposed here is robust, efficient, easy to implement and computationally very attractive.

Particle Based Smoothed Marginal MAP Estimation for General State Space Models

We consider the smoothing problem for a general state space system using sequential Monte Carlo (SMC) methods. The marginal smoother is assumed to be available in the form of weighted random particles from the SMC output. New algorithms are developed to extract the smoothed marginal maximum a posteriori (MAP) estimate of the state from the existing marginal particle smoother. Our method does not need any kernel fitting to obtain the posterior density from the particle smoother. The proposed estimator is then successfully applied to find the unknown initial state of a dynamical system and to address the issue of parameter estimation problem in state space models.

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space SystemsWe review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of anirreducible-at-infinitygeneralized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts ofirreducibilityandminimalityof generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts ofdynamicandnon-dynamicvariables appearing in generalized state space realizations are also examined.

Exponential estimation of generalized state-space time-delay systems

In this paper, global exponential stability for a class of generalized state-space time-delay systems is considered. Delay-dependent criteria are proposed to guarantee the exponential stability and estimate the convergence rate for the generalized state-space systems with two cases of uncertainties. Finally, some numerical examples are illustrated to show the usefulness of the theory.

Haar wavelet method for the analysis of transistor circuits

This paper presents Haar wavelet based method of analysis for observer design in the generalized state space or singular system of transistor circuits. The technique can be interpreted from the incremental and multiresolution view point. Accurate solutions can be obtained by changing the time scale ( m ) , at the same time the main features of the solution are preserved. It can be easily implemented with a digital computer and it is found to be fast, flexible, convenient and computationally attractive.

Stability margins for generalized state space systems

In this work we extend results from the literature on H ∞ design with pole placement constraints to the case of generalized state space models, for both continuous-time and discrete-time systems. We also propose tests using linear matrix inequalities of reduced dimension.

Positivity and Linear Matrix Inequalities

In this paper we first recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for some particular applications in systems and control. Finally, we indicate how these problems can be solved numerically and what specific numerical difficulties can be encountered in these applications.

On the solution and impulsive behaviour of polynomial matrix descriptions of free linear multivariable systems

In this note we examine the solution and the impulsive behaviour of autonomous linear multivariable systems whose pseudo-state beta(t) obeys a linear matrix differential equation A(rho)beta(t) = 0 where A(rho) is a polynomial matrix in the differential operator rho:=d/dt. We thus generalize to the general polynomial matrix case some results obtained by Verghese and colleagues which regard the impulsive behaviour of the generalized state vector x(t) of input free generalized state space systems.

Lowering the Orders of Input Shifts in Discrete-Time Generalized State-Space Systems

Abstract The problem of lowering the orders of input forward shifts in generalized state space systems by generalized state transformations is studied through the language of differential forms. Necessary and sufficient conditions are given for the local existence of such transformation. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for finding these generalized state transformations. In particular case, these conditions show when it is possible to transform a generalized state space representation into the classical state equations.

Meeting transfer function requirements via static measurement output feedback

The important transfer function design problems of input-output decoupling, exact model matching and disturbance rejection, via static measurement output feedback, are studied for the case of generalized state space systems. Necessary and sufficient conditions for the solvability of these problems are established. The general analytical expressions of the respective controller matrices are derived. The above results are also extended to cover the combined problem of disturbance rejection with simultaneous decoupling and the problem of disturbance rejection with simultaneous exact model matching.

A matrix-pencil-based interpretation of inconsistent initial conditions and system properties of generalized state-space systems

Division of Computer Science, Department of Electrical and Computer Engineering,National Technical University of Athens, Zographou, 15773, Athens, GreeceA matrix-pencil-based approach is presented to interpret transition matrices,inconsistent initial conditions, and systems properties of regular generalized state-space (GSS) systems. On the basis of the well known Weierstrass canonical form ofa regular pencil, several definitions of transition matrices for GSS systems aregiven. Convolution forms of the forced state evolution of GSS systems are also estab-lished, both for the case of consistent and of inconsistent initial conditions. Moreover,a fundamental interpretation of inconsistent initial conditions of GSS systems isoutlined. Finally, the notion of several types of controllability and observabilityGramians of GSS systems is introduced. Relations of these Gramians to the respec-tive controllability and observability properties of GSS systems are examined, andsimple and easily checked algebraic criteria based on these Gramians, are estab-lished. It is pointed out that these results appear to be first in the field o f GSS systems.

Dynamic Precompensation for the Discrete Time Control Design of Continuous Time Generalized State Space Systems

ABSTRACTThis paper deals with the discrete time control design of continuous time generalized state space systems. The use of numerical controllers has largely developed this kind of control device. Considering generalized state space systems, a particular attention must be paid of to the choice of the hold device. In fact, for a non convenient one, impulsive behaviours disturb the system response after the initial time. The aim of this work is to prevent the arising of such behaviours. A dynamic precompensator is first proposed to smooth out the input corresponding to a 0-order hold function. A class of generalized sampled data hold functions is then derived.

Exact Unidirectional Perturbation Bounds for Robustness of Uncertain Generalized State-Space Systems: Continuous-Time Cases

Abstract The robustness of continuous-time generalized state-space systems with unidirectional perturbations is investigated in this paper. By transforming the original problem to a robust rank problem, we provide a simple method to compute the exact bounds on such perturbations so that the important features of regularity, impulse immunity, and stability of nominal systems are all preserved. This approach can be viewed as a generalization of Fu and Barmish's result to generalized state-space setups. It also provides a tractable solution to many practical robustness problems. This is clearly explained by a simple circuit example. © 1997 Elsevier Science Ltd.

Block Decoupling of Generalized State Space Systems

The problem of input-output block decoupling of generalized state space systems, via a regular static state feedback law, is studied for the first time. The necessary and sufficient conditions for the problem to have a solution are established. The necessary and sufficient conditions for block decoupling with simultaneous stabilizability , and the necessary and sufficient conditions for block decoupling with simultaneous arbitrary assignment of the system poles are established. © 1997 Elsevier Science Ltd.

Feedback design and precompensation for generalized systems

Feedback control designs are useful for removing the impulses that disturb the behavior of generalized state space systems. The aim of this paper is to detail the design of dynamic precompensators for the implementation of such feedback control designs. Necessary and sufficient conditions are given so that the resulting regulators are biproper. It is pointed out that these conditions are restrictive and that feedback control designs can lead to nonproper precompensators. To overcome this difficulty, a class of proper precompensators is proposed. These regulators, which result from an adaptation of the Silverman structure algorithm, remove the impulse behaviors that occur after the initial time by smoothing out the input vector.

Limits of generalized state space systems under proportional and derivative feedback

In this paper we study the high-gain feedback classification problem for generalized state space systems. We solve this problem for proportional and derivative feedback transformations of regularizable systems, i.e., we give necessary and sufficient conditions for a regularizable system to be a limit of a given system under high-gain proportional and derivative feedback. We also derive a new complete set of invariants for proportional feedback equivalence and specify a set of necessary conditions for a system to be the limit of another system under these feedback transformations. The necessary conditions are sufficient for arbitrary state space systems and for controllable singular systems.