一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.     

A controller perturbation technique for transferring closed-loop stability between systems

This brief paper presents a perturbation technique with which a controller stabilizing one plant may be modified so that it stabilizes a second, related plant. The proposed technique produces an internally stable loop for a broad class of linear systems without requiring any further calculations on the part of the designer. Four seemingly different examples are described in terms of this result.     

Time-domain input-output representations of linear systems

A non-oriented matrix pencil model containing internal and external variables is shown to possess properties useful for modelling and design of linear dynamical systems. Three of these properties are trivial inversion, invariance under a useful class of operations, and simple decomposition using easily-implemented row and column operations. Realizations of state-space and polynomial operator models are given, then a definition of system dimension and a minimal-reduction algorithm. A new time-domain canonical form compatible with polynomial operator systems is described. Examples of the use of the model in algebraic design problems are given.     

Local parametrizations of ARMAX systems with nonlinear restrictions

A necessary and sufficient condition of local identifiability is derived by using the well-known Rank Theorem. Using this condition a suitable local parametrization is defined. The topological and geometrical properties of this parametrization are investigated. The results obtained generalize the corresponding results of Deistler and Wang (1989), which deal with essentially the systems with linear restrictions. The treatment covers also the systems without a priori restrictions.     

求解规范型Lyapunov矩阵方程的新方法

本文揭示了规范型Lyapunov矩阵方程及其对偶方程的一些特殊性质,充分压缩解矩阵的未知元素,并利用对偶解矩阵与解矩阵的合同关系,提出了一种高精度、高效率求解规范型Lyapunov方程的新算法,文中举例验证了新算法的正确性。 Lyapunov矩阵方程 能控制和能观测规范型 单输入单输出系统     

Complete Controllability Conditions for a Linear Nonstationary System in a Critical Case

The paper presents complete controllability conditions for a linear nonstationary system when the rank of the Krasovskii matrix is lower than the system dimension. The results supplement the results obtained by N. N. Krasovskii, A. Chang, A. A. Levakov, S. A. Minyk, and I. V. Gayshun.     

Uniquely identifiable state-space and ARMA parametrizations for multivariable linear systems

Multivariable systems can be represented, in a uniquely identifiable way, either by canonical forms or by so-called overlapping forms. The advantage of the latter is that they do not require the a priori estimation of a set of structural invariants (e.g. Kronecker invariants). We show here how to define uniquely identifiable overlapping parametrizations for state-space and ARMA models. We show that these parametrizations are all related to a set of intrinsic invariants, which are obtained from the Markov parameters of the system. Different forms of overlapping ARMA parametrizations are derived and their properties discussed.     

Numerical analysis of the reduction of linear systems into orthogonal canonical form

An efficient numerically stable computational algorithm for reduction of linear systems into orthogonal canonical form is described. The algorithm is based on QR decomposition with column pivoting. Exact error bounds and operation count for the algorithm are derived.     

Input-output finite time stabilization of linear systems

Bounded Input Bounded Output (BIBO) stability is usually studied when only the input-output behavior of a dynamical system is of concern. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS (IO-FTS). FTS has been already investigated in several papers in terms of state boundedness, whereas in this work we deal with the characterization of the input-output behavior. Sufficient conditions are given, concerning the class of L₂ and L_∞ input signals, for the analysis of IO-FTS and for the design of a static state feedback controller, guaranteeing IO-FTS of the closed-loop system. The effectiveness of the proposed results is eventually illustrated by means of some numerical examples.     

On the stability of slowly time-varying linear systems

New conditions are given in both deterministic and stochastic settings for the stability of the system x=A(t)x when A(t) is slowly varying. Roughly speaking, the eigenvalues of A(t) are allowed to wander into the right half-plane as long as on average they are strictly in the left half-plane.This work was funded by the NSF under Grant ECS-8806063, and was completed while the author was with the Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218, U.S.A.     

Stability robustness for linear state space models - a Lyapunov mapping approach

Some Pythagorean-like conditions for the existence of a common Lyapunov solution for two given matrices are presented. These conditions are set on the Lyapunov mappings associated with given matrices. The key is the semipositiveness of linear mappings defined on symmetric matrices. From the viewpoint of the existence of a common Lyapunov solution, some known stability robustness results are reviewed and refined.     

Invariants and canonical forms for systems structural and parametric identification

The basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled.With reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set.Then the set of polynomial input-output models of the type P(z)y(t)=Q(z)u(t) and the equivalence relation induced by the premultiplication of P and Q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced.Since the two sets of canonical forms share common sets of complete independent invariants, very simple algebraical links between state space and input-output canonical forms can be deduced.The previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input-output sequences generated by a linear, discrete, time-invariant multivariable system.The results obtained in the identification of a real process are then reported.     

Strong feedback cyclization for systems over rings

For nonnecessarily reachable systems over a commutative ring R, we define a strong form of feedback cyclization (FC). With this natural generalization of the FC property we obtain a feedback reduced form for systems over strong FC rings (i.e. rings for which every system verifies the FC property). In the particular case of reachable single input systems, this gives the usual control canonical form of Bumby et al. [Remarks on the pole-shifting problem over rings, J. Pure Appl. Algebra 20 (1981) 113–127]. Also it is proved that a commutative ring with 1 in its stable range has the strong FC property if and only if it has the UCU property, which is the natural parallel form of the result given by Brewer et al. [Pole assignability in polynomial rings, power series rings and Prüfer domains, J. Algebra 106 (1987) 265–286] for the reachable case. Many classes of rings which were known to be FC rings are in fact strong FC rings, but there are FC rings which are not strong FC rings.