Disturbance Decoupling in Nonlinear Impulsive Systems

International audienceThis work deals with the problem of structural disturbance decoupling by state feedback for nonlinear impulsive systems. The dynamical systems addressed exhibit a hybrid behavior characterized by a nonlinear continuous-time state evolution interrupted by abrupt discontinuities at isolated time instants. The problem considered consists in finding a state feedback such that the system output is rendered totally insensitive to the disturbance. Both the case of static state feedback and that of dynamic state feedback are considered. A necessary and sufficient condition for the existence of a static state feedback that solves the problem in the multivariable case is proven by defining suitable tools in the context of the differential geometric approach. The situation concerning solvability by a dynamic state feedback is examined in the framework of the differntial algeraic approach. A necessary and sufficient solvaility condition is conjectured and discussed

On the zeros and poles of a transfer function

AbstractThe poles and zeros of a linear transfer function can be studied by means of the pole module and the transmission zero module. These algebraic constructions yield finite dimensional vector spaces whose dimensions are the number of poles and the number of multivariable zeros of the transfer function. In addition, these spaces carry the structure of a module over a ring of polynomials, which gives them a dynamical or state space structure. The analogous theory at infinity gives finite dimensional spaces which are modules over the valuation ring of proper rational functions. Following ideas of Wedderburn and Forney, we introduce new finite dimensional vector spaces which measure generic zeros which arise when a transfer function fails to be injective or surjective. A new exact sequence relates the global spaces of zeros, the global spaces of poles, and the new generic zero spaces. This sequence gives a structural result which can be summarized as follows: “The number of zeros of any transfer function is equal to the number of poles (when everything is counted appropriately).” The same result unifies and extends a number of results of geometric control theory by relating global poles and zeros of general (possibly improper) transfer functions to controlled invariant and controllability subspaces (including such spaces at infinity)

An efficient computation of the solution of the Block Decoupling Problem with Coefficient Assignment over a ring

The paper presents procedures to check solvability and to compute solutions to the Block Decoupling Problem over a Noetherian ring and procedures to compute a feedback law that assigns the coefficients of the compensated system while mantaining the decoupled structure over a Principal Ideal Domain. The algorithms have been implemented using MapleV® and CoCoA

ON FAMILIES OF SYSTEMS: POINTWISE-LOCAL-GLOBAL ISOMORPHISM PROBLEMS

Let E and E' be two families of linear dynamical systems, or, almost equivalently, let E and E' be two systems over a ring. This paper addresses itself to the question, what, if anything, can be said about the relations between E and E' if it is known that E and E' are pointwise isomorphic for all or almost all of the parameter values

Multi-agent system theory for resource management in home automation systems

A paradigm for modelling and analysing Home Automation Systems is introduced, based on Multi-Agent System theory. A rich and versatile environment for Home Automation System simulation is constructed for investigating the performances of the system. The exploitation of limited resources (electricity, gas, hot water) depends on behavioural parameters of the individual appliances. In order to deal with the problem of developing systematic design and validation procedures for control strategies, global performance indices for the system are introduced. Different strategies for allocating resources and establishing priorities in their use can therefore be tested and compared