On the decoupling of one class of multivariable systems
On the development of SCILAB compatible software for the analysis and control of repetitive processes
In this paper further results on the development of a S CILAB compatible software package for the analysis and control of repetitive processes is described. The core of the package consists of a simulation tool which enables the user to inspect the response of a given example to an input, design a control law for stability and/or performance, and also simulate the response of a controlled process to a specified reference signal.
On the equivalence conditions of two-stage and direct identification methods
On the equivalence of control systems on Lie groups
We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.
On the essential instabilities caused by fractional-order transfer functions.
On the exact controllability of a nonlinear stochastic heat equation.
On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients
Let be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...
On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients
Let be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke's generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...
On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.
System similarity and system strict equivalence concepts from Rosenbrock's theory on linear systems are used to establish algebraic conditions of model matching as well as an algebraic method for design of centralized compensators. The ideas seem to be extensible without difficulty to a class of decentralized control.
On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems
In this paper, we consider the well-known Fattorini’s criterion for approximate controllability of infinite dimensional linear systems of type y′ = Ay + Bu. We precise the result proved by Fattorini in [H.O. Fattorini, SIAM J. Control 4 (1966) 686–694.] for bounded input B, in the case where B can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini’s criterion is satisfied and if the set of geometric multiplicities of A is bounded then approximate...
On the genericity of the observability of controlled discrete-time systems
In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.
On the genericity of the observability of controlled discrete-time systems
In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.
On the identification of diffusion coefficients
On the interaction between theory experiments and simulation in developing practical learning control algorithms
Iterative learning control (ILC) develops controllers that iteratively adjust the command to a feedback control system in order to converge to zero tracking error following a specific desired trajectory. Unlike optimal control and other control methods, the iterations are made using the real world in place of a computer model. If desired, the learning process can be conducted both in the time domain during each iteration and in repetitions, making ILC a 2D system. Because ILC iterates with the real...
On the -instability and -controllability of steady flows of an ideal incompressible fluid
In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady flow is unstable...
On the lack of null-controllability of the heat equation on the half space.
On the links between limit characteristic zeros and stability properties of linear time-invariant systems with point delays and their delay-free counterparts.
On the Lyapunov equation in Banach spaces and applications to control problems.
On the Morgan problem with stability
On the nature of descriptor systems