1,721,008 research outputs found
Extreme eigenvalues of large sparse matrices by Rayleigh quotient and modified conjugate gradients
No full textA structural approach to unknown inputs observation for switching linear systems
Full text linkThe problem of devising an asymptotic observer for a given function of the state of a switching linear system in the presence of unknown inputs is considered. Solvability is studied both in the case of sufficiently large dwell time and in that of dwell time greater than a fixed threshold. A complete characterization of solvability in terms of necessary and sufficient conditions is given in both cases. It is shown that the necessary and sufficient conditions can be checked in practice in the first case and, under slightly more restrictive hypotheses, also in the second case by means of algorithmic procedures, which also provide a method to synthesize the observer sought for. The employed methodology makes use of geometric concepts to reveal the structural aspects of the problem and to derive its solutions. In particular, a key role is played by the novel notion of robust conditioned invariant subspace that is minimal with respect to the properties of containing a given subspace and of being externally stabilizable
Asymptotic Model Matching for LPV Systems
No full textWe consider the problem of forcing the output of a given Linear Parameter Varying (LPV) plant to match asymptotically that of a given LPV model using a static or a dynamic feedback control law that also quadratically stabilizes the plant. The problem is investigated from a structural point of view and solvability conditions are expressed in geometric terms. Under suitable hypotheses, checkable sufficient conditions and viable procedures for constructing solutions are provided
Disturbance decoupling and model matching problems for discrete-time systems with time-varying delays
Full text linkIn this paper, the disturbance decoupling problem and the model matching problem for discrete-time linear systems with time-varying delays are considered. Solvability of the above problems is characterized by means of structural necessary and sufficient conditions that can be checked by algorithmic procedures. The basic method used to analyze the considered problems consists in representing the discrete-time linear systems with time-varying delays as switching linear systems, whose properties can be studied by a powerful structural approach. In this way, the considered control problems can be reduced to the corresponding problems for switched linear systems, whose solvability has been recently characterized
Disturbance Decoupling in Nonlinear Impulsive Systems
No full textThis 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
Results in the Structural-Geometric Approach to Switching Linear Systems
No full textIn this survey we present recent results on switching linear systems. In particular, we recall structural-geometric notions of invariance, controlled invariance and conditioned invariance for switching linear systems and we show how they can be used to provide solutions to a number of control and application problems
Disturbance decoupling with stability for impulsive switching linear systems
No full textThis paper deals with the problem of decoupling the output of a hybrid system from a disturbance input by means of a switching state feedback, which, at the same time, stabilizes, in a suitable sense, the compensated system. The class of hybrid systems considered consists of impulsive switching linear systems, that is switching linear systems whose state exhibits impulsive discontinuities, called jumps, at the switching instants. Switching is assumed to be time-driven and the distance between consecutive switching instants is assumed to be lower bounded by some positive number. Structural geometric methods and tools are used to investigate the decoupling problem and to study feedback stabilizability. Necessary and sufficient solvability conditions are given in the case in which the distance between consecutive switching instants can be assumed to be sufficiently large. A sufficient solvability condition is also provided in the case in which the lower bound for such distance is assigned
Unknown-input state observers with minimal order for linear impulsive systems
No full textThis paper deals with the problem of asymptotically estimating a linear function of the state of a linear impulsive system, in the presence of unknown inputs, by means of an observer whose state space has the minimal possible dimension. The linear impulsive systems considered are subject to the following constraint: the length of the time interval between any two consecutive jumps must be greater than or equal to a given finite positive constant. First, a necessary and sufficient condition for the existence of an observer whose state space has a generic dimension (i.e., not necessarily minimal) is proven. Then, the issue of the minimization of the observer state dimension is investigated and solved
Output regulation of discrete-time systems with time-varying delays
No full textIn this paper the output regulation problem for discrete-time linear systems with time-varying delays is considered. Solvability of the above problem is completely characterized in structural geometric terms and a sufficient condition that can be practically checked, together with a procedure to construct solutions, if any exists, is given. The basic method used to analyze the considered problem consists in representing the discrete-time linear systems with time-varying delays as switching linear systems, whose properties can be studied by a powerful structural approach. In this way, the considered problem can be reduced to the corresponding problem for switched linear systems, whose solvability has been recently characterized
A class of reset linear systems: the reset-delayed linear systems and their structural and stability properties
Full text linkThis work introduces a new class of reset linear systems, called reset-delayed linear systems, which consists of multivariable dynamical systems featuring a continuous-time state evolution interrupted by discontinuities of some, or even all the state variables at isolated time instants. In particular, these discontinuities abide by an algebraic equation imposing that the state variables involved take the same values they respectively had a certain amount of time before the time instant when the discontinuity is triggered. In this way, the evolutions of the state variables involved turn out to be delayed by the amount of time considered in the reset operation. In the presence of suitably chosen forcing actions, reset-delayed linear systems can effectively model repetitive behaviors which imply a discontinuity at the junction between one cycle and the subsequent one. Herein, some structural properties of this class of multivariable linear dynamical systems are studied and the geometric notions of invariance and controlled invariance are formalized and applied to the solution of the disturbance decoupling problem
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