Teorie katastrof: souvislosti a aplikace. II
The algebraic output feedback in the light of dual-lattice structures
The purpose of this paper is to derive constructive necessary and sufficient conditions for the problem of disturbance decoupling with algebraic output feedback. Necessary and sufficient conditions have also been derived for the same problem with internal stability. The same conditions have also been expressed by the use of invariant zeros. The main tool used is the dual- lattice structures introduced by Basile and Marro [R4].
The asymptotical stability of a dynamic system uppercasewith structural damping
A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.
The boundary crossing theorem and the maximal stability interval.
The choice of the forms of Lyapunov functions for a positive 2D Roesser model
The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^{T}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.
The eigenvalue derivatives of linear damped systems
The equivalence of controlled lagrangian and controlled hamiltonian systems
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems
The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics.
The finite inclusions theorem: a tool for robust design
Methods for robust controller design, are an invaluable tool in the hands of the control engineer. Several methodologies been developed over the years and have been successfully applied for the solution of specific robust design problems. One of these methods, is based on the Finite Inclusions Theorem (FIT) and exploits properties of polynomials. This has led to the development of FIT-based algorithms for robust stabilization, robust asymptotic tracking and robust noise attenuation design. In this...
The geometrical quantity in damped wave equations on a square
The energy in a square membrane Ω subject to constant viscous damping on a subset decays exponentially in time as soon as ω satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate of this decay satisfies (see Lebeau [Math. Phys. Stud.19 (1996) 73–109]). Here denotes the spectral abscissa of the damped wave equation operator and is a number called the geometrical quantity of ω and defined as follows. A ray in Ω is the trajectory generated by the free motion...
The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem.
The La Salle invariance principle for multidimensional dynamical systems
The nonlinear regulator problem for constant signals
The order reduction and robust D-stability analysis of discrete uncertain time-delay systems by time-scale separation
The stability of an irrigation canal system
In this paper we examine the stability of an irrigation canal system. The system considered is a single reach of an irrigation canal which is derived from Saint-Venant's equations. It is modelled as a system of nonlinear partial differential equations which is then linearized. The linearized system consists of hyperbolic partial differential equations. Both the control and observation operators are unbounded but admissible. From the theory of symmetric hyperbolic systems, we derive the exponential...
The stabilization problem on surfaces.
The truncation method for the solution of a class of variational inequalities
The uncertainty problem in control theory. II. The internally robust procedures
Time optimal control of a second order nonlinear plant