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The stability of feedback systems consisting of linear time-delay plants and PID controllers has been investigated for many years by means of several methods, of which the Nyquist criterion, a generalization of the Hermite-Biehler Theorem,…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
The stabilization of nonautonomous parabolic equations is achieved by feedback inputs tuning a finite number of actuators, where it is assumed that the input is subject to a time delay. To overcome destabilizing effects of the time delay,…
We develop delay-compensating feedback laws for linear switched systems with time-dependent switching. Because the future values of the switching signal, which are needed for constructing an exact predictor-feedback law, may be unavailable…
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…
Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean-Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of…
Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this paper we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger…
This paper presents and implements an iterative feedback design algorithm for stabilisation of discrete-time switched systems under arbitrary switching regimes. The algorithm seeks state feedback gains so that the closed-loop switching…
This note proposes a data-driven output-feedback stabilizing policy iteration for unknown linear discrete-time systems with unmeasurable states. Existing policy iteration methods for optimal control must start from a stabilizing control…
This paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based…
We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
This paper presents a Lyapunov-Halanay method to study global asymptotic stabilization (GAS) of nonlinear retarded systems subject to large constant delays in input/output - a challenging problem due to their inherent destabilizing effects.…
In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping…
Delayed feedback control is an easy realizable control method which generates control force by comparing the current and the delayed version of the system states. In this paper, a new form of the delayed feedback structure is introduced.…
The double barrier resonant tunneling diode exhibits complex spatio-temporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time--delayed feedback control can…
Reduced-order models for flows that exhibit time-periodic behavior are critical for several tasks, including active control and optimization. One well-known procedure to obtain the desired reduced-order model in the proximity of a periodic…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…