摘要:

Eigenstructure assignment for continuous-time descriptor systemsEx(t)=Ax(t)+Bu(t) via descriptor-variable feedback controlu(t)=Kx(t) is treated. A new parametric form for the gain matrixKwhich assigns rank [E] arbitrary finite eigenvalues to the closed-loop system is developed. This form embraces two sets of design parameter vectors characterizing respectively the assignable eigenvectors associated with the finite eigenvalues and a necessary and sufficient condition for closed-loop system regularity. In addition, a certain submatrix ofKturns out to be totally free whenever nullity [E] exceeds rank [B]. Unlike earlier methods, the eigenvectors associated with the infinite eigenvalues are dispensed with in the solution algorithm.

ISSN:0020-7179    

DOI:10.1080/00207178908559625

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The discrete-time minimum variance filtering of continuous-time processes and the duality between the problems of discretized filtering and regulation are considered. The discrete-time optimal filter consists of a digital algorithm which is applied to the prefiltered sampled measurements. This algorithm is based on the overall discrete- time equivalent model (i.e. the continuous-time process, the prefilter and the sampler). For the first time, different formulations of this discrete-time equivalent model are presented in a comprehensive unified way. A few prevailing misunder- standings of the discretization issue are clarified and a few errors that appear in the literature are corrected. The equations that govern the optimal linear quadratic discrete-time regulation of continuous-time systems are presented. By comparing these equations to the equations that have been obtained for the optimal filtering problem we show that the optimal discretized filtering problem is not dual to the corresponding problem of the discretized optimal regulation.

ISSN:0020-7179    

DOI:10.1080/00207178908559626

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The set of open-loop (right) block-diagonalizers of a givenp?mtransfer matrixZ, with specified block sizes, is studied. A characterization of this set is obtained in terms of a'maximal' open-loop block-diagonalizer and a minimal proper basis of the kernel ofZ. The relevance of the results to some non-interacting control problems is pointed out. In particular, the results obtained yield a minimum delay solution to the block-decoupling problem using dynamic state feedback.

ISSN:0020-7179    

DOI:10.1080/00207178908559627

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The reduction of order of high-order models obtained from an identification experiment is discussed from a statistical point of view. The asymptotic maximum likelihood (ML) approach is defined to reduce the order of an estimated model. This approach considers the maximum likelihood criterion given the asymptotic statistics (both in the number of data and the order) of the estimated model, and corresponds to frequency weightedL2-norm model reduction. By using the insight from the asymptotic ML approach, an identification algorithm is proposed based on a high- order ARX estimate and model reduction via a frequency weighted balanced realization. The advantage of this algorithm is that iterative minimization methods are not required to find the estimate.

ISSN:0020-7179    

DOI:10.1080/00207178908559628

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Generalized conditions for the existence of periodic strong solutions in periodically time-varying matrix Riccati equations are derived. First, the precise structure of eigenvalues on the unit circle of the transition matrix associated with the hamil- tonian matrix and that of the corresponding generalized eigenvectors are clarified in relation to the (quasi-) detectability and (quasi-) stabilizability of the system. Then such analysis is applied for deriving the conditions for the existence of a unique, periodic, real, symmetric and non-negative definite solution in the periodically time- varying matrix Riccati equation.

ISSN:0020-7179    

DOI:10.1080/00207178908559629

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Balanced realizations of linear time-invariant singularly perturbed systems are studied. The reduced model of a singularly perturbed system that is obtained, based on the balanced realization, is compared to that obtained by time-scale considerations. An approximate balancing transformation for singularly perturbed systems is constructed based on balancing transformations of the approximating slow and fast subsystems.

ISSN:0020-7179    

DOI:10.1080/00207178908559630

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A geometrically inspired matrix algorithm is derived for the identification of statespace models for multivariable linear time-invariant systems using (possibly noisy) input-output (I/O) measurements only. As opposed to other (mostly stochastic) identification schemes, no variance-covariance information whatever is involved, and only a limited number of I/O-data are required for the determination of the system matrices. Hence, the algorithm can be best described and understood in the matrix formalism, and consists of the following two steps. First, a state vector sequence is realized as the intersection of the row spaces of two block Hankel matrices, constructed with I/O-data. Then the system matrices are obtained at once from the least-squares solution of a set of linear equations. When dealing with noisy data, this algorithm draws its excellent performance from repeated use of the numerically stable and accurate singular value decomposition. Also, the algorithm is easily applied to slowly time-varying systems using windowing or exponential weighting. These results are illustrated by examples, including the identification of an industrial plant.

ISSN:0020-7179    

DOI:10.1080/00207178908559631

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The problem of eigenstructure assignment via the dynamical compensator of linear systems is dealt with. The sufficient and necessary conditions of permissible radical systems is advanced and compensators of different order are discussed. The minimal order bounds of compensators and a minimal algorithm are given. Several examples are worked out to explain the structure of assignable vectors and the given algorithm.

ISSN:0020-7179    

DOI:10.1080/00207178908559632

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

An algorithm is presented for solving the strengthened discrete-time 1-block model-matching problem. All the steps of the algorithm are performed using state-space models and each step has a closed-form solution. The uniqueness of the super- optimal solution follows from the constructions in the algorithm. Although the problem is analogous to the continuous-time case and the strategy used is the same, there are some intricate differences in detail which make the derivation of one from the other non-trivial. By working completely in discrete-time, the super-optimal controller can be analysed explicitly in thez-domain and implemented directly on a digital computer.

ISSN:0020-7179    

DOI:10.1080/00207178908559633

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions. Two classes of conjugations are shown to be important. One is the lossless conjugation that performs inner-outer factorization and the other is theJ-lossless conjugation that solves the model-matching problem related toH8-control. The solution of the model-matching problem obtained byJ-lossless conjugation is regarded as the state-space version of the directional interpolation theory, and is much simpler than those obtained via the Nehari approximation.

ISSN:0020-7179    

DOI:10.1080/00207178908559634

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor