5,502 research outputs found
Lagrangian submanifolds in affine symplectic geometry
We uncover the lowest order differential invariants of Lagrangian
submanifolds under affine symplectic maps, and find out what happens when they
are constant.Comment: 23 pages, no figure
Analysis and Design of Complex-Valued Linear Systems
This paper studies a class of complex-valued linear systems whose state
evolution dependents on both the state vector and its conjugate. The
complex-valued linear system comes from linear dynamical quantum control theory
and is also encountered when a normal linear system is controlled by feedback
containing both the state vector and its conjugate that can provide more design
freedom. By introducing the concept of bimatrix and its properties, the
considered system is transformed into an equivalent real-representation system
and a non-equivalent complex-lifting system, which are normal linear systems.
Some analysis and design problems including solutions, controllability,
observability, stability, eigenvalue assignment, stabilization, linear
quadratic regulation (LQR), and state observer design are then investigated.
Criterion, conditions, and algorithms are provided in terms of the coefficient
bimatrices of the original system. The developed approaches are also utilized
to investigate the so-called antilinear system which is a special case of the
considered complex-valued linear system. The existing results on this system
have been improved and some new results are established.Comment: 19 page
Regulation and robust stabilization: a behavioral approach
In this thesis we consider a number of control synthesis problems within the behavioral approach to systems and control. In particular, we consider the problem of regulation, the H! control problem, and the robust stabilization problem. We also study the problems of regular implementability and stabilization with constraints on the input/output structure of the admissible controllers. The systems in this thesis are assumed to be open dynamical systems governed by linear constant coefficient ordinary differential equations. The behavior of such system is the set of all solutions to the differential equations. Given a plant with its to-be-controlled variable and interconnection variable, control of the plant is nothing but restricting the behavior of the to-be-controlled plant variable to a desired subbehavior. This restriction is brought about by interconnecting the plant with a controller (that we design) through the plant interconnection variable. In the interconnected system the plant interconnection variable has to obey the laws of both the plant and the controller. The interconnected system is also called the controlled system, in which the controller is an embedded subsystem. The interconnection of the plant and the controller is said to be regular if the laws governing the interconnection variable are independent from the laws governing the plant. We call a specification regularly implementable if there exists a controller acting on the plant interconnection variable, such that, in the interconnected system, the behavior of the to-becontrolled variable coincides with the specification and the interconnection is regular. Within the framework of regular interconnection we solve the control problems listed in the first paragraph. Solvability conditions for these problems are independent of the particular representations of the plant and the desired behavior.
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