Class Of Discrete-time Bilinear Systems Research Articles

Structural controllability and structural near-controllability of a class of discrete-time bilinear systems

In this paper, we consider the structural controllability problems of a class of driftless discrete-time bilinear systems which have nearly the same structure as linear systems. Algebraic as well as graph-theoretic conditions for structural controllability of such systems with single-input and multi-input are, respectively, obtained. Furthermore, we introduce a new notion, called structural near controllability, for those structured systems which cannot be structurally controllable but structurally nearly-controllable. It is shown that the bilinear systems can be structurally nearly-controllable although their linear counterparts can never have a large controllable region no matter what the parameters are chosen. Necessary and sufficient conditions for structural near-controllability of the bilinear systems are thus derived. We also consider the structural controllability problem in the continuous-time case. Examples and graphs are given to illustrate the obtained results of this paper.

On the existence of complex roots of real polynomials

This paper is concerned with the existence problem of complex roots of real polynomials with degree , which is derived from the study of near-controllability of a class of discrete-time bilinear systems. Some sufficient conditions for the existence of complex roots are presented, which are easy to apply.

On Computing Control Inputs to Achieve State Transition for a Class of Nearly Controllable Discrete-time Bilinear Systems

Near-controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been well demonstrated on discrete-time bilinear systems. The purpose of this paper is to propose a useful algorithm to compute the control inputs, which achieve the transition of a given pair of states, for a class of discrete-time bilinear systems that are nearly controllable. Accordingly, for such class of bilinear systems, not only near-controllability is proved, but also the computability of control inputs for near-controllability is shown. An example is provided to demonstrate the effectiveness of the proposed algorithm.

On Near-Controllability, Nearly Controllable Subspaces, and Near-Controllability Index of a Class of Discrete-Time Bilinear Systems: A Root Locus Approach

This paper studies near-controllability of a class of discrete-time bilinear systems via a root locus approach. A necessary and sufficient criterion for the systems to be nearly controllable is given. In particular, by using the root locus approach, the control inputs which achieve the state transition for the nearly controllable systems can be computed. Furthermore, for the non-nearly controllable systems, nearly-controllable subspaces are derived and near-controllability index is defined. Accordingly, the controllability properties of such class of discrete-time bilinear systems are fully characterized. Finally, examples are provided to demonstrate the results of the paper.

A root locus approach to near-controllability of a class of discrete-time bilinear systems with applications to Hermitian matrices

In this paper, a root locus approach is developed to investigate near-controllability of a class of discrete-time bilinear systems and new representations of Hermitian matrices are derived. The root locus approach has three merits: firstly, it makes the proof of near-controllability of the systems more simple; secondly, the control inputs that achieve the state transition can be computed in an explicit way and, meanwhile, the number of the required control inputs can be fixed; and thirdly, it leads to a more general conclusion on near-controllability. A numerical example is given to demonstrate the effectiveness of the root locus approach. Finally, the more general conclusion yields new representations of Hermitian matrices.

On nearly-controllable subspaces of a class of discrete-time bilinear systems

If a linear time-invariant system is uncontrollable, then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace. In this paper, for a class of discrete-time bilinear systems which are uncontrollable but can be nearly controllable, by studying the nearly-controllable subspaces and defining the near-controllability index, the controllability properties of the systems are fully characterized. Examples are provided to illustrate the conceptions and results of the paper.

On near-controllability and stabilizability of a class of discrete-time bilinear systems

In this paper, the near-controllability and stabilizability of a class of discrete-time bilinear systems are studied. A necessary and sufficient condition for the near-controllability of the systems is first derived. Then, on the basis of the corresponding near-controllability criterion, the stabilizability problem of the systems is solved in turn.

On controllability of discrete-time bilinear systems

In this paper, necessary and sufficient conditions for the controllability of a class of discrete-time bilinear systems are proposed, which extend the existing results and show that the controllability counterexample in [1] that is derived by Euler discretization of an uncontrollable bilinear system, is a special case of the necessary and sufficient conditions.

KYP lemma, state feedback and dynamic output feedback in discrete-time bilinear systems

This paper shows how a generalization of the Kalman-Yacubovitch-Popov (KYP) lemma can be built for discrete-time bilinear passive systems, and how the concepts of passivity and feedback equivalence can be applied to solve the problem of global stabilization via smooth state feedback, bounded state feedback and dynamic output feedback for a class of discrete-time bilinear systems. The results generalize some recent advances due to Gauthier and Kupka (1992) in continuous-time bilinear systems to their discrete-time counterparts.

Second-order correlation method for bilinear system identification

An algorithm is developed to estimate parameters of a class of discrete-time bilinear systems using second-order correlations. It is shown that for pseudorandom binary and ternary input signals the computations in the estimation algorithm can be simplified. The method is compared with least-squares algorithm for a model of nuclear fission. The proposed algorithm gives a computationally simple and effective way of parameter estimation.