Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping.
Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems
This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for...
Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation
Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation
The concepts of stability, attractivity and asymptotic stability for systems subject to restrictions of the input values are introduced and analyzed in terms of Lyapunov functions. A comparison with the well known input-to-state stability property introduced by Sontag is provided. We use these concepts in order to derive sufficient conditions for global stabilization for triangular and feedforward systems by means of saturated bounded feedback controllers and also recover some recent results...
Input-to-state stability of neutral type systems
We consider the system (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems,...
Input-to-state stability with respect to measurement disturbances for one-dimensional systems
Input-to-state stability with respect to measurement disturbances for one-dimensional systems
We consider one-dimensional affine control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed affine.
Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach
This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference...
Interior feedback stabilization of wave equations with time dependent delay.
Internal properness and stability in linear systems
Invariant sets of hybrid autonomous systems with disturbance.
Invariant subspaces for grasping internal forces and non-interacting force-motion control in robotic manipulation
This paper presents a parametrization of a feed-forward control based on structures of subspaces for a non-interacting regulation. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e. g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics and general mechanisms may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural...
Invariant tracking
The problem of invariant output tracking is considered: given a control system admitting a symmetry group , design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of . Invariant output errors are defined as a set of scalar invariants of ; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required...
Invariant tracking
The problem of invariant output tracking is considered: given a control system admitting a symmetry group G, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of G. Invariant output errors are defined as a set of scalar invariants of G; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the...
Inverse optimal control for linearizable nonlinear systems with input delays
We consider inverse optimal control for linearizable nonlinear systems with input delays based on predictor control. Under a continuously reversible change of variable, a nonlinear system is transferred to a linear system. A predictor control law is designed such that the closed-loop system is asymptotically stable. We show that the basic predictor control is inverse optimal with respect to a differential game. A mechanical system is provided to illustrate the effectiveness of the proposed method....
Inverse optimal dynamic boundary control for uncertain Korteweg-de Vries-Burgers equation
We investigate Korteweg-de Vries-Burgers (KdVB) equation, where the dissipation and dispersion coefficients are unknown, but their lower bounds are known. First, we establish dynamic boundary controls with update laws to globally exponentially stabilize this uncertain system. Secondly, we demonstrate that the dynamic boundary control design is suboptimal to a meaningful functional after some minor modifications of the dynamic boundary controls. In addition, we also consider dynamic boundary controls...
Jeden typ jednoparametrových nelineárnych číslicových regulačných obvodov
L2 performance induced by feedbacks with multiple saturations
Multi-level saturation feedbacks induce nonlinear disturbance-to-state L2 stability for nonlinear systems in feedforward form. This class of systems includes linear systems with actuator constraints.
Large scale dynamic system stabilization using the principle of dominant subsystems approach
Leader-following consensus of multiple linear systems under switching topologies: An averaging method
The leader-following consensus of multiple linear time invariant (LTI) systems under switching topology is considered. The leader-following consensus problem consists of designing for each agent a distributed protocol to make all agents track a leader vehicle, which has the same LTI dynamics as the agents. The interaction topology describing the information exchange of these agents is time-varying. An averaging method is proposed. Unlike the existing results in the literatures which assume the LTI...