S.-I. Niculescu

Robust exponential stability of uncertain systems with time-varying delays

Focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time-varying delays. The uncertainties are assumed to be continuous time-varying, nonlinear, and norm bounded. Sufficient conditions for robust exponential stability are given for both single and multiple delays cases.

Robust stabilization for uncertain time-delay systems containing saturating actuators

A class of uncertain time-delay systems containing a saturating actuator is considered. These systems are characterized by delayed state equations (including a saturating actuator) with norm-bounded parameter uncertainty (possibly time varying) in the state and input matrices. The delay is assumed to be constant bounded but unknown. Using a Razumikhin approach for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws. These bounds are given in terms of solutions of appropriate finite dimensional Riccati equations.

Delay-dependent stability of linear systems with delayed state: an LMI approach

This paper deals with the problem of asymptotic stability of a class of time-delay systems with constant, but unknown time-delay. Upper bounds on the time-delay that ensure the stability of the considered systems are given using a Razumikhin technique. Furthermore, the approach adopted here allows the computation of the delay bound by transforming the stability problem into an LMI optimization problem.

Dynamical compensation for time‐delay systems: an LMI approach

This paper presents simple and explicit formulae of an ‘observer-based H∞ controller’ for linear time-delay systems. Based on the LMI approach, we design a dynamical controller which guarantees the asymptotic stability of the closed-loop system and reduces the effect of the perturbation to a prescribed level. The main contribution of the paper is to provide closed-loop stability analysis when the system time delay is unknown. We give delay-dependent and delay-independent stability results. The proposed method is illustrated by examples. The paper completes the work of the same authors. Copyright

On tracking control of a class of complementary-slackness hybrid mechanical systems

Abstract In this note we consider the problem of feedback control of n-dof (degree-of-freedom) rigid manipulators subject to a scalar frictionless unilateral constraint f(X)⩾0 (X∈ R n is the vector of generalized coordinates). The stability analysis relies on a stability concept that incorporates the hybrid and nonsmooth dynamical feature of the overall system. It is shown that stability of the closed-loop system can be obtained. This work generalizes the results in [Brogliato et al. (IEEE Trans. Automat. Control 42(2) (1997) 200–215)] which were mainly restricted to the 1-dof case. It also clarifies some concepts related to the hybrid nature of closed-loop complementary-slackness mechanical systems.

Delay robustness of closed loop finite assignment for input delay systems 1

Abstract The problem of the robustness with respect to delay uncertainty for the finite spectrum closed loop assignment of input delay systems is addressed. Numerically exploitable conditions in terms of the maximal deviation of the design delay, and of the assigned closed loop are given. An analytic expression of a lower bound of this deviation guaranteeing stability in the monovariable and multivariable case are obtained. The Smith predictor and related schemes are also revisited.

Control of some distributed delay systems using generalized popov theory

Abstract The paper deals with the generalized Popov theory applied to systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for γ - attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov - Krasovskii functional. The considered approach is new in the context of distributed linear-delay systems and gives some interesting interpretations of H ∞ memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples.

Delay effects and dynamical compensation for time-delay systems

We develop an observer-based H/sup /spl infin// controller for linear time delay systems. The main contribution is to provide a closed loop stability analysis for the general case when the system time delay is unknown. Our analysis is based on model transformation and on a comparison principle. This allows us to get delay dependent stabilizing conditions. We derive conditions which improve (or recover) previous results. Comments on the conservatism of the presented criteria are given. The approach makes use of appropriate Liapunov-Krasovskii functionals and the obtained criteria are expressed in terms of linear matrix inequalities. A numerical example illustrates this method.

H/sub /spl infin// memoryless control with an /spl alpha/-stability constraint for time-delays systems: an LMI approach

This note focuses on the design of H/sub /spl infin// memoryless state feedback controllers satisfying some /spl alpha/-stability constraints on the closed-loop poles for a class of linear systems with delayed state subject to disturbance inputs. A sufficient condition for feasibility is derived in terms of linear matrix inequalities. Furthermore, the author also considers a particular optimization problem: the maximal bound allowed on time-delay such that the prescribed level on disturbance attenuation and the /spl alpha/-stability constraints are still preserved. This problem is converted into an LMI optimization problem and the author gives a suboptimal bound on the delay.

ON ROBUST STABILITY VIA COMPLETE LYAPUNOV KRASOVSKII FUNCTIONAL

Abstract Stability of linear systems with norm-bounded uncertainties and uncertain time-varying delays is considered. The delays are supposed to be bounded and fast-varying (without any constraints on the delay derivative). Sufficient stability conditions are derived via complete Lyapunov-Krasovskii functional (LKF). A new LKF construction, which was recently introduced for systems with uncertain delays, is extended to the case of norm-bounded uncertainties: to a nominal LKF, which is appropriate to the system with the nominal value of the coefficients and of the delays, terms are added that correspond to the perturbed system and that vanish when the uncertainties approach 0. Numerical examples illustrate the efficiency of the method.