This paper provides an overview of recent results for relay-delay systems. In a first section, simple examples illustrate the problems induced by delays in the synthesis of sliding mode controllers. Then, a brief overview of the existing results shows the present advances and limits in this domain. The last parts of the paper are devoted to new results: first, for systems with state delay, then...

In a recent paper we presented the first adaptive control design for an ODE system with a possibly large actuator delay of unknown length. We achieved global stability under full state feedback. In this paper we generalize the design to the situation where, besides the unknown delay value, the ODE also has unknown parameters, and where trajectory tracking (rather than equilibrium regulation) is...

We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems. Our method circumvents the problem of constructing and estimating distributed terms in the control laws, and allows arbitrarily large input delay bounds, pointwise time-varying input delays, and uncertainties. Instead of using distributed terms, our approach to handling longer delay...

In this paper, we describe a stabilization method for linear time-delay systems which extends the classical pole placement method for ordinary di7erential equations. Unlike methods based on :nite spectrum assignment, our method does not render the closed loop system, :nite dimensional but consists of controlling the rightmost eigenvalues. Because these are moved to the left half plane in a (qua...

We discuss a nite horizon H∞ control problem for time-varying systems with input delays. Clarifying a relationship between two H∞ control problems in input delay case and in measurement delay case, we derive a solution in input delay case based on the known result for the H∞ control problem in measurement delay case, and show that the solution has the same predictor–observer structure as the so...

In this paper, we present an explicit solution to H∞ full-information control for discrete-time systems with multiple input delays. Our solution is given in terms of one standard Riccati difference equation of the same order as the plant under investigation. Thus, it has much computational advantage over methods such as system augmentation. As special cases, solutions to the H∞ control problem ...

This paper discusses the stabilization of Takagi–Sugeno (T–S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T–S fuzzy input delay systems without uncertainties. A separate design princip...

lag is a general term applied to coarse grained (> 2 mm), hard, but partially weathered rockfragments, which are concentrated at the surface through attrition of finer materials. based on morphology,mineralogy and the origin of lag from the cobar region of australia, lag may be conveniently grouped intothree broad morpho-mineralogical categories; (a) those with a rough, blocky, lithic morpholog...

We present a new stabilization approach for nonlinear plants with a long input delay. The stabilization problem is complicated by the influence of an uncertain biased sinusoidal disturbance. The problem of control design is solved with using measurable state variables. The adaptive scheme allows to identify the frequency and other parameters of the external disturbance that are used in a reject...

This note is concerned with the problem of semi-globally stabilizing a linear system with an input delay and a constraint on the energy of its input. Under the condition of null controllability with vanishing energy, the parametric Lyapunov equation based L2 low gain feedback is adopted to solve the problem. The proposed approach is applied to the linearized model of the relative motion in the ...