Exponential stability of a nonlinear distributed parameter system.
Exponential stability of time-switched two-subsystem nonlinear systems with application to intermittent control.
Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks*
In this paper, the stability of a Timoshenko beam with time delays in the boundary input is studied. The system is fixed at the left end, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system is well-posed. By the complete spectral analysis, we show that there is a sequence of eigenvectors and generalized eigenvectors of the system operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies the spectrum...
Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks*
In this paper, the stability of a Timoshenko beam with time delays in the boundary input is studied. The system is fixed at the left end, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system is well-posed. By the complete spectral analysis, we show that there is a sequence of eigenvectors and generalized eigenvectors of the system operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies the spectrum...
Exponential stability of two coupled second-order evolution equations.
Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics
Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics
Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was first addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These...
Exponentially dissipative nonlinear dynamical systems: A nonlinear extension of strict positive realness.
Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems
We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show...
External stabilization of discontinuous systems and nonsmooth control Lyapunov-like functions.
Factorization of the Popov function of a multivariable linear distributed parameter system in the non-coercive case: a penalization approach
We study the construction of an outer factor to a positive definite Popov function of a distributed parameter system. We assume that is a non-negative definite matrix with non-zero determinant. Coercivity is not assumed. We present a penalization approach which gives an outer factor just in the case when there exists any outer factor.
Falseness of the finiteness property of the spectral subradius
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...
Fault Tolerant Control design for polytopic LPV systems
This paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both fault-free and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary)...
Fault tolerant control for uncertain time-delay systems based on sliding mode control
Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some linear matrix inequalities (LMIs), delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can...
Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching
This paper investigates the problem of fault tolerant control of a class of uncertain switched nonlinear systems with time delay under asynchronous switching. The systems under consideration suffer from delayed switchings of the controller. First, a fault tolerant controller is proposed to guarantee exponentially stability of the switched systems with time delay. The dwell time approach is utilized for stability analysis and controller design. Then the proposed approach is extended to take into...
Fault-tolerant pitch-rate control augmentation system design for asymmetric elevator failures in a combat plane
Combat planes are designed in a structured relaxed static stability to meet maneuver requirements. These planes are unstable in the longitudinal axis and require continuous active control systems with elevator control. Therefore, failures in the elevator can have vital consequences for flight safety. In this work, the performance of classical control approach against asymmetric elevator failures is investigated and it is shown that this approach is insufficient in the case of such a failure. Then,...
Feedback control of time-delay systems with bounded control and state.
Feedback controller stabilizing vibrations of a flexible cable related to an overhead crane.
Feedback linearization of control for nonlinear systems with uncertainties
Feedback stabilization of a boundary layer equation
We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminar-to-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate linear parabolic equation. Because of the degenerate character of the state equation, the classical existence...