Showing papers on "Positive systems published in 2005"

Control for stability and positivity: equivalent conditions and computation

Abstract: This paper investigates the stabilizability of linear systems with closed-loop positivity. A necessary and sufficient condition for the existence of desired state-feedback controllers guaranteeing the resultant closed-loop system to be asymptotically stable and positive is obtained. Both continuous and discrete-time cases are considered, and all of the conditions are expressed as linear matrix inequalities which can be easily verified by using standard numerical software. Numerical examples are provided to illustrate the proposed conditions.

Controllability and reachability of 2-D positive systems: a graph theoretic approach

Abstract: When dealing with two-dimensional (2-D) discrete state-space models, controllability properties are introduced in two different forms: a local form, which refers to single local states, and a global form, which instead pertains the infinite set of local states lying on a separation set. In this paper, these concepts are investigated in the context of 2-D positive systems by means of a graph theoretic approach. For all these properties, necessary and sufficient conditions, which refer to the structure of the digraph, are provided. While the global reachability index is bounded by the system dimension n, the local reachability index may far exceed the system dimension. Upper bounds on the local reachability index for some special classes of positive systems are finally derived.

Transient Effects of Linear Dynamical Systems

Abstract: Cauchy problem, 19, 136 Condition number, 40, 55, 99, 110 Contractibility, 183 Counterflow equation, 156 Critical delay, 167 Delay Liapunov function, 138 Delay margin, 170 Departure from normality, 56 Diagonalizable matrix, 55 Diagonally dominant matrix, 36 Differential inclusion, 45 Dissipativity radius, 33 Dual norm, 8, 25 Dual pair, 25 Eccentricity, 39–43 Eigenpair, 59 Field of values, 34 Front locus, 85 Gershgorin set, 34 Growth rate asymptotic, 20 initial, 20, 30, 37 Hermitian matrix pencil, 71 Hilbert direct sum, 12 Implicit Euler step, 17, 77 Inverse power method, 74 Kreiss constant, 79 Kronecker product, 161 Liapunov cone, 101 Liapunov operator, 99, 192 Liapunov vector, 112, 118 Liapunov-Krasovskii functional, 143 Linear fractional transformation, 80 Linear operator, 11 adjoint, 14 block-diagonal, 12 coercive, 14 dissipative, 27 normal, 14 positive, 14 self-adjoint, 14 Metzler matrix, 108 Metzler part of a matrix, 121 Mild solution, 19 Norm dual, see dual norm Feller, 40, 94–99 Liapunov, 38 monotone, 8 operator, 9 p-norm, 8 polytopic, 104 smooth, 9 transient, 40 Numerical radius, 9 Numerical range, 34 Operator, see linear operator Perron vector, 108 Perturbation structure, 10 Positive orthant, 107 Projection Stereographic, 80 Pseudospectral abscissa, 10 Pseudospectrum, 11 Rayleigh quotient, 34

Stability Radii of Linear Systems Under Multi-perturbations

Abstract: In this paper, we study stability radii of linear systems under multi-perturbation of the coefficient matrices. Formulas for complex stability radius are derived. We then consider linear positive systems and prove that for this class of systems, the complex stability radius is equal to the real stability radius which can be computed via a simple formula. We illustrated the obtained results by two examples.

Realization problem for a class of positive continuous-time systems with delays

Abstract: In positive systems, inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, or water and atmospheric pollution models. A variety of models revealing the behaviour of positive linear systems can be found in engineering, management science, economics, social sciences, biology and medicine, etc.

Stability of positive linear discrete-time systems

Abstract: The main focus of the paper is on the asymptotic behaviour of linear discrete-time positive systems. Emphasis is on highlighting the relationship between asymptotic stability and the structure of the system, and to expose the relationship between null-controllability and asymptotic stability. Results are presented for both time-invariant and time-variant systems.

On Controllability of Timed Continuous Petri Net Systems: the Join Free Case

Abstract: Timed continuous PNs have been used as relaxed models to evaluate `approximately' the performance of the underlying discrete systems. Moreover, the control of the continuized systems can approximate the scheduling of the (discrete) PNs. This paper analyses the controllability of conservative and consistent join free net systems under infinite server semantics. They are positive systems in which classic control theory is not directly applicable: in this domain input actions are non-negative and dynamically bounded, leading to polytope constrained state space instead of a vectorial space. Thus a new concept of controllability is proposed. The `controllability space' (CS), included in this polytope, is studied depending on the set of controlled transitions. The full state space is `controllable' iff all the transitions are controlled. On the other hand, a given state can always be `controlled' (reached and maintained) without using all transitions. The CS obtained by controlling just one transition is a straight segment, and the CS obtained with several transitions includes the convex of the CS obtained independently with every transition. If additionally the system is choice-free the state space is a partition of the CS obtained with the entire set of transitions except one. Nevertheless borders belong to all neighbour regions.

A Polynomial Matrix Approach to the Structural Properties of 2D Positive Systems

Abstract: In this paper, (local/global) reachability and observability are introduced in the context of two-dimensional (2D) positive systems. While local reachability and observability are naturally characterized by resorting to certain real matrices associated with the 2D state space representation, their global versions are better investigated via a polynomial approach. Necessary and sufficient conditions for the existence of these properties are provided and, in particular, polynomial canonical forms for globally reachable/observable positive systems with scalar inputs/scalar outputs are provided