38,180 research outputs found
Finite-time behavior of inner systems
In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller
Nonsquare Spectral Factorization for Nonlinear Control Systems
This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton–Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system.
Grushin problems and control theory: Formulation and examples
In this paper we give a new formulation of an abstract control problem in
terms of a Grushin problem, so that we will reformulate all notions of
controllability, observability and stability in a new form that gives readers
an easy interpretation of these notions
Properties of recoverable region and semi-global stabilization in recoverable region for linear systems subject to constraints
This paper investigates time-invariant linear systems subject to input and state constraints. It is shown that the recoverable region (which is the largest domain of attraction that is theoretically achievable) can be semiglobally stabilized by continuous nonlinear feedbacks while satisfying the constraints. Moreover, a reduction technique is presented which shows, when trying to compute the recoverable region, that we only need to compute the recoverable region for a system of lower dimension which generally leads to a considerable simplification in the computational effort
A general realization theorem for matrix-valued Herglotz-Nevanlinna functions
New special types of stationary conservative impedance and scattering
systems, the so-called non-canonical systems, involving triplets of Hilbert
spaces and projection operators, are considered. It is established that every
matrix-valued Herglotz-Nevanlinna function of the form
V(z)=Q+Lz+\int_{\dR}(\frac{1}{t-z}-\frac{t}{1+t^2})d\Sigma(t) can be realized
as a transfer function of such a new type of conservative impedance system. In
this case it is shown that the realization can be chosen such that the main and
the projection operators of the realizing system satisfy a certain
commutativity condition if and only if L=0. It is also shown that with
an additional condition (namely, is invertible or L=0), can be realized as
a linear fractional transformation of the transfer function of a non-canonical
scattering -system. In particular, this means that every scalar
Herglotz-Nevanlinna function can be realized in the above sense.
Moreover, the classical Livsic systems (Brodskii-Livsic operator
colligations) can be derived from -systems as a special case when
and the spectral measure is compactly supported. The realization
theorems proved in this paper are strongly connected with, and complement the
recent results by Ball and Staffans.Comment: 28 page
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 -spectral factorization. One of these conditions is in terms of equalizing vectors. A second one states that the existence of a -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 -spectral factorization in terms of the Hamiltonian is added
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