Recently, attention has been focused on the class of bilinear systems, both for its applicative interest and intrinsic simplicity. In fact, it appears that many important processes, not only in engineering, but also in biology, socio-economics, and ecology, may be modeled by bilinear systems. Moreover, since their nonlinearity is due to products between input and state variables, this class frequently may be studied by techniques similar to those employed for linear systems. This work is intended to motivate the interest of bilinear systems and to present the current state of research in its various aspects. After an introductory section, in which theoretical and applicative aspects of bilinear systems are enlightened, four other sections follow, respectively, devoted to structural properties, mathematical models, identification and optimization. In a final section, some concluding remarks are made on still open problems and possible trends for future research.

Bilinear systems: An appealing class of "nearly linear" systems in theory and applications

In this paper the controllability of a class of discrete time bilinear systems is discussed. Necessary and sufficient conditions for complete controllability are derived. In addition a complete characterization of the controllable regions of this class of systems, when not completely controllable, is made.

https://ieeexplore.ieee.org/iel5/9/24158/01101408.pdf

Controllability of a class of discrete time bilinear systems

Controllability of time-invariant discrete-time bilinear systems is discussed. Bilinear systems are classified into two categories: homogeneous and inhomogeneous. Sufficient conditions which ensure the global controllability of discrete-time bilinear systems are obtained by localized analysis in control variables.

Controllability of discrete bilinear systems with bounded control

Papers on optimal, control theory, reviewed in Referativnyi Zhurnal “Matematika” during 1971–1975, are surveyed.

Mathematical theory of optimal control

State and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition (QEPCAD) symbolic computation program. The method is unified for a very large class of systems and can handle one- or two-sided control constraints. Families of minimum time state/output dead beat controllers are obtained. The computational complexity of the test is prohibitive for general polynomial systems, but by constraining the structure of the system we may beat the curse of complexity. A computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented. Necessary and sufficient conditions are given. They are still very difficult to check. Therefore, a number of easier-to-check sufficient conditions are also provided. The latter are based on the Grobner basis method and QEPCAD. It is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system.

/pdf/dead-beat-controllability-of-polynomial-systems-symbolic-lq1hln9pmx.pdf

T. Goka

Papers

On the controllability of a class of discrete bilinear systems