Vladimir Suplin

H/sub /spl infin// control of linear uncertain time-delay systems-a projection approach

The issues of stability and H/sub /spl infin// control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finslers projection lemma, delay-dependent sufficient conditions are obtained, in terms of linear matrix inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H/sub /spl infin// state-feedback control.

Input/output delay approach to robust sampled-data H∞ control

Sampled-data output-feedback H∞ control of linear systems is considered. The only restriction on the sampling and hold is that the distances between the sequel sampling times and holding times are not greater than given bounds. A new approach, which was recently introduced to sampled-data state-feedback stabilization, is developed to the H∞ control. The system is modelled as a continuous-time one, where the control input and the measurement output have piecewise-continuous delays. Sufficient linear matrix inequalities (LMIs) conditions for H∞ control of such systems are derived via Lyapunov–Krasovskii functionals and descriptor approach to time-delay systems. For the first time the new approach allows to develop different robust control methods for the case of sampled-data H∞ control.

Stability of linear systems with general sawtooth delay

It is well known that in many particular systems, the upper bound on a certain time-varying delay that preserves the stability may be higher than the corresponding bound for the constant delay. Moreover, sometimes oscillating delays improve the performance (Michiels, W., Van Assche, V. & Niculescu, S. (2005) Stabilization of time-delay systems with a controlled time-varying delays and applications. IEEE Trans. Automat. Control, 50, 493–504). Sawtooth delays τ with τ = 1 (almost everywhere) can posses this property (Louisell, J. (1999) New examples of quenching in delay differential equations having time-varying delay. Proceedigns of the 5th ECC, Karlsruhe, Germany). In this paper, we show that general sawtooth delay, where τ 6= 0 is constant (almost everywhere), also can posses this property. By the existing Lyapunov-based methods, the stability analysis of such systems can be performed in the framework of systems with bounded fast-varying delays. Our objective is to develop ‘qualitatively new methods’ that can guarantee the stability for sawtooth delay which may be not less than the analytical upper bound on the constant delay that preserves the stability. We suggest two methods. One method develops a novel input–output approach via a Wirtinger-type inequality. By this method, we recover the result by Mirkin (2007, Some remarks on the use of time-varying delay to model sample-and-hold circuits. IEEE Trans. Automat. Control, 52, 1109–1112) for τ = 1 and we show that for any integer τ , the same maximum bound that preserves the stability is achieved. Another method extends piecewise continuous (in time) Lyapunov functionals that have been recently suggested for the case of τ = 1 in Fridman (2010, A refined input delay approach to sampled-data control. Automatica, 46, 421–427) to the general sawtooth delay. The time-dependent terms of the functionals improve the results for all values of τ , though the most essential improvement corresponds to τ = 1.

A new bounded real lemma representation for the continuous-time case

A differential linear matrix inequality (DLMI) approach is introduced for the solution of various linear continuous-time control problems. The proposed method permits the application of linear matrix inequalities (LMIs) to the solution of control design problems under uncertainty. These problems are solved for finite horizon linear systems while considerably reducing the overdesign inherent in previous methods. The new approach also allows for the solution of the output-feedback control problem for systems belonging to a finite set of uncertain plants with hardly any overdesign. Four examples are given to demonstrate the applicability of the new method.

Robust H∞ output-feedback control of systems with time-delay

Abstract The problem of designing robust dynamic output-feedback controllers for linear, continuous, time-invariant systems with uncertain time-delay in the measured output and/or the control input and with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state–space model of the system is described which permits reconstruction of its states. The resulting retarded model incorporates the uncertain parameters of the transfer function matrix in the state–space matrices and the uncertain time-delay that occurs in the control channel. To this model, the recent theory of robust H ∞ state-feedback control for retarded systems is applied. The theory is used to solve a benchmark problem of distillation column robust control design.

H ∞ sampled data control of systems with time-delays

Sampled-data Hinfin control of linear systems with state, control and measurement constant delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input-output approach to stability and L2-gain analysis is applied to the resulting system. The discretized Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (in the input and in the output), which are unknown, time-varying with known upper-bounds. Solutions to the state-feedback and the output- feedback Hinfin control problems are derived in terms of linear matrix inequalities (LMIs).

Robust H∞ output-feedback control of linear discrete-time systems

The problem of designing H∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.

Robust H∞H∞ output-feedback control of linear discrete-time systems ☆

The problem of designing H∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.

Mixed H/sub /spl infin///H/sub 2/ design of digital phase locked loops with polytopic type uncertainties

A robust H/sub /spl infin// control method is applied to the design of loop filters for digital phase locked loop carrier phase tracking. The proposed method successfully copes with large S-curve slope uncertainty and with a significant decision delay in the closed loop that may stem from the decoder and/or the equalizer there. The design problem is transformed into a state-feedback control problem where phase and gain margins should be guaranteed in spite of the uncertainty. Of all the loop filters that achieve the required margins the one that minimizes an upper-bound on the effect of the phase and the measurement noise signals is derived.