Computational issues in fault detection filter design

We discuss computational issues encountered in the design of residual generators for dynamic inversion based fault detection filters. The two main computational problems in determining a proper and stable residual generator are the computation of an appropriate leftinverse of the fault-system and the computation of coprime factorizations with proper and stable factors. We discuss numerically reliable approaches for both of these computations relying on matrix pencil approaches and recursive pole assignment techniques for descriptor systems. The proposed computational approach to design fault detection filters is completely general and can easily handle even unstable and/or improper systems

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.

Asymptotically fast polynomial matrix algorithms for multivariable systems

We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer algebra techniques, minimal basis computations and matrix fraction expansion/reconstruction, and to polynomial matrix multiplication. Such reductions eventually imply that all these problems can be solved in about the same amount of time as polynomial matrix multiplication

J-spectral factorization and equalizing vectors

For the Wiener class of matrix-valued functions we provide necessary and sufficient conditions for the existence of a $J$-spectral factorization. One of these conditions is in terms of equalizing vectors. A second one states that the existence of a $J$-spectral factorization is equivalent to the invertibility of the Toeplitz operator associated to the matrix to be factorized. Our proofs are simple and only use standard results of general factorization theory. Note that we do not use a state space representation of the system. However, we make the connection with the known results for the Pritchard-Salamon class of systems where an equivalent condition with the solvability of an algebraic Riccati equation is given. For Riesz-spectral systems another necessary and sufficient conditions for the existence of a $J$-spectral factorization in terms of the Hamiltonian is added

Bitangential interpolation in generalized Schur classes

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 47 page