Controllability and Gramians of 2D Continuous Time Linear Systems (original) (raw)

Controllability Analysis of Two-dimensional Systems Using 1D Approaches

IEEE Transactions on Automatic Control, 2015

Working with the 1D form of 2D systems is an alternative strategy to reduce the inherent complexity of 2D systems and their applications. To achieve the 1D form of 2D systems, different from the so-called WAM model, a new row (column) process was proposed recently. The controllability analysis of this new 1D form is explored in this paper. Two new notions of controllability named WAM-controllability and directional controllability for the underlying 2D systems are defined. Corresponding conditions on the WAM-controllability and directional controllability are derived, which are particularly useful for the control problems of 2D systems via 1D framework. According to the presented directional controllability, a directional minimum energy control input is derived for 2D systems. A numerical example demonstrates the applicability of the analysis presented in this note.

Controllability of dynamical systems. A survey

Bulletin of the Polish Academy of Sciences: Technical Sciences, 2013

The main objective of this article is to review the major progress that has been made on controllability of dynamical systems over the past number of years. Controllability is one of the fundamental concepts in the mathematical control theory. This is a qualitative property of dynamical control systems and is of particular importance in control theory. A systematic study of controllability was started at the beginning of sixties in the last century, when the theory of controllability based on the description in the form of state space for both time-invariant and time-varying linear control systems was worked out. Roughly speaking, controllability generally means, that it is possible to steer a dynamical control system from an arbitrary initial state to an arbitrary final state using the set of admissible controls. It should be mentioned, that in the literature there are many different definitions of controllability, which strongly depend on a class of dynamical control systems and o...

Controllability of Continuous Bimodal Linear Systems

Mathematical Problems in Engineering, 2013

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions.

Controllability of second order linear systems

Let (A 1 , A 2 , B) be a triple of matrices representing two-order time-invariant linear systems,ẍ = A 1ẋ +A 2 x+Bu. Using linearization process we study the controllability of second order linear systems. We obtain sufficient conditions for controllability and we analyze the kind of systems verifying these conditions.

On controllability of linear systems

The classical theory of controllability for deterministic systems is extended to linear stochastic systems defined on infinite dimensional Hilbert spaces. Three types of stochastic controllability are studied: approximate, exact and Ë-controllability. Tests for exact, approximate and Ëcontrollabilities are proved and relation between the controllability of linear stochastic systems and the controllability of the corresponding deterministic systems is studied

Control theory for a class of 2D continuous-discrete linear systems

International Journal of Control, 2004

This paper considers a general class of 2D continuous-discrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and operator setting. In particular, important new results are developed on stability, controllability, stabilization, and optimal control.

Reachability, Observability and Minimality for a Class of 2D Continuous-Discrete Systems

2007

Reachability and observability criteria are obtained for 2D continuous-discrete time-variable Attasi type systems by using suitable 2D reachability and observability Gramians. Necessary and sufficient conditions of reachability and observability are derived for time-invariant systems. The duality between the two concepts is emphasized as well as their connection with the minimality of these systems.

Controllability, observability, realizability, and stability of dynamic linear systems

2009

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from the recent work . We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We explore observability in terms of both Gramian and rank conditions and establish related realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.