一般化多項式による中立型むだ時間システムの解析とその極設定および非干渉制御への応用

In this paper, both problems of the stability and stabilization analysis for linear neutral time-delay systems are respectively investigated. The time-delays considered here are assumed bounded but no information to be available. Using Lyapunov functional method, delay-dependent conditions for the stability and stabilization of the systems are presented in terms of linear matrix inequality (LMI). A numerical example is given to illustrate the main results of this paper and make a comparison with the results presented in literatures

In this note, we study the stability properties of linear neutral delay systems. We consider systems described by both neutral differential-difference and state-space equations, and we seek to determine the delay margin of such systems, that is, the largest range of delay values for which a neutral delay system may preserve its stability. In both cases, we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices, which can be executed efficiently and with high precision. The results extend previously known work on retarded systems, and demonstrate that similar stability tests exist for neutral systems; in particular, the tests require essentially the same amount of computation required for retarded systems.

A robust sliding mode control strategy with virtual state feedback is presented for the neutral time-delay systems. The virtual state feedback control is designed to avoid the complicated non-linear matrix inequality. Furthermore, a delay-independent sufficient condition for the design of a robust stable sliding mode plane is obtained in terms of linear matrix inequality (LMI). A brief sliding mode controller is designed to guarantee state trajectories from any initial condition are attracted to the sliding mode plane in a finite time and remain there for all subsequent time. The stability of the sliding mode control system is also guaranteed. A numerical example with simulation results is given to illustrate the effectiveness of the methodology.

Computing nearby non-trivial Smith forms

In the present paper is presented a numerical method for the exact reduction of a singlevariable polynomial matrix to its Smith form without finding roots and without applying unimodular transformations. Using the notion of compound matrices, the Smith canonical form of a polynomial matrixM(s)∈ℝnxn[s] is calculated directly from its definition, requiring only the construction of all thep-compound matricesCp(M(s)) ofM(s), 1<p≤n. This technique produces a stable and accurate numerical algorithm working satisfactorily for any polynomial matrix of any degree.

Constrained Feedback Control of Imperfectly Known, Linear, Time-Delay Systems of Neutral Type

Cooperative output regulation problem for linear time-delay multi-agent systems under switching network

Equivalence and reduction of bivariate polynomial matrices to their Smith forms

Spaces of multiparameter rational vectors, i.e., of vectors whose components are rational functions in several variables, and polynomial bases of their subspaces are considered. The conjecture that any subspace in the space of multiparameter rational vectors possesses a “free” polynomial basis, i.e., a basis such that the associated basis multiparameter polynomial matrix has no finite regular spectrum, is disproved by an example. Some consequences of this fact are indicated. Simpler proofs of some properties of the singular spectra of basis polynomial matrices corresponding to the null-spaces of a singular polynomial matrix are presented. Bibliography: 5 titles.

The problems of realization and feedback stabilization of autonomous linear neutral systems are studied in the context of linear systems over commutative rings. Connections are made to the theory of retarded delay systems as well as to generalized linear systems over a field.

Embedding, i.e expanding a nonsquare matrix to a square one, plays a significant role in systems and control theory. For instance, embedding a polynomial matrix P(î) unimodularlyallowed us to solve the pole placement problem in chapter 3 and stable embedding(a less restrictive version) yielded a solution for the stabilization problem.In this chapter we will discuss existing and new algorithms1 to solve the embedding problem. The scope of the chapter is as follows. In section 5.1 we define the problem and give some motivating examples, in section 5.2 we give an overview of existing algorithms to solve the embedding problem, and we give a couple of examples to show that the method based on the Smith form does not give acceptable answers. After that we turn to the algorithm of Beelen [4],[5] based on matrix pencils. In section 5.3 we introduce matrix pencils, in section 5.4 we relate the embedding problem for an arbitrary polynomial matrix to one for a pencil by using a state space representation. In section 5.5 we give the solution for the embedding problem for a pencil, section 5.6 describes the way to calculate that solution, in section 5.7 we describe the algorithm that gives a unimodular or stable embedding starting from a polynomial matrix.

In this article, delay-dependent stability criteria for linear retarded and neutral systems with multiple delays are proposed by employing the Lyapunov-Krasovskii functional approach and integral inequality. By the N-segmentation of delay length, we obtain more relaxed results on the delay bounds which guarantee the asymptotic stability of the linear retarded and neutral systems with multiple delays. Simulation results show that the stability boundary calculated by the proposed stability criteria are very near to the real stability boundary of the example systems. Moreover, it is shown that the proposed stability criteria are less conservative than several other existing criteria.

This paper deals with the problem of positive observation for linear time-delay systems for which the states take nonnegative values whenever the initial conditions are nonnegative. We focus on the design of positive observers (possibly with time-delay) which guarantee nonnegative estimates of the current states. We derive necessary and sufficient conditions for the existence of a positive observer (extended Luemberger-type) and show that the solvability of the problem can be decided via standard linear programming techniques. Moreover, on the negative side, it is shown that one cannot stabilize any unstable positive time-delay system by using extended Luenberger type positive observers. In other words, the separation principle does not hold.

In this paper, a theory of polynomial and rational matrix interpolation is introduced and applied to problems in systems and control. The polynomial matrix interpolation theory is first outlined and then applied to solving matrix equations; it is also used in pole assignment and other control problems. Rational matrix interpolation is also discussed and it is used to solve rational matrix equations including the model matching problem.

A simple approach to synthesizing a proportional and derivative state feedback gain for assigning poles to infinity is developed. We also apply the synthesized gain to determine a doubly coprime matrix fraction description (MFD) of a state-space system and solve related problems. It is interesting to note that the MFD and the solutions to the related problems could be obtained in an explicit formula by using the synthesized gain.