Guest editorial introduction to the two special issues on advances in analysis and control of time-delay systems
control of discrete-time linear systems constrained in state by equality constraints
In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task....
sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities
This paper is devoted to design sliding mode controller for continuous-time Markov jump systems with interval time-varying delays and general transition probabilities. An integral sliding surface is constructed and its reachability is guaranteed via a sliding mode control law. Meanwhile, a linearisation strategy is applied to treat the nonlinearity induced by general transition probabilities. Using a separation method based on Finsler lemma to eliminate the coupling among Lyapunov variables and...
Hierarchical sliding mode control for a class of SIMO under-actuated systems
Homogeneous approximations and local observer design
This paper is concerned with the construction of local observers for nonlinear systems without inputs, satisfying an observability rank condition. The aim of this study is, first, to define an homogeneous approximation that keeps the observability property unchanged at the origin. This approximation is further used in the synthesis of a local observer which is proven to be locally convergent for Lyapunov-stable systems. We compare the performance of the homogeneous approximation observer with the...
Hybrid dynamical systems vs. ordinary differential equations: Examples of "pathological" behavior.
Hybrid robust stabilization in the Martinet case
Hybrid stabilization of discrete-time LTI systems with two quantized signals
We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of...
Immunotherapy with interleukin-2: A study based on mathematical modeling
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
Improved results on robust stability analysis and stabilization for a class of uncertain nonlinear systems.
Improved robust stability criteria of uncertain neutral systems with mixed delays.
Improving the performance of semiglobal output controllers for nonlinear systems
For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers with increasing regions of attraction is that, when the region of attraction is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some...
Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold
Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system...
Impulse control in Kalman-like filtering problems.
Impulsive exponential stabilization of functional differential systems with infinite delay.
Independence of asymptotic stability of positive 2D linear systems with delays of their delays
It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
Indirect stabilization of locally coupled wave-type systems
We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...
Indirect stabilization of locally coupled wave-type systems
We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...
Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping.
Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems
This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for...