Section: New Results

Non-Linear, Sampled And Time-Delay Systems

Nonlinearities, sampling, quantization and time-delays cause serious obstructions for control and observer design in many fields of techniques and engineering (e.g. networked and internet systems, distributed systems etc.). The proposed by the team algebraic approach suits well for estimation and regulation in such a type of systems. The recent results are listed below:

• The method of Implicit Lyapunov-Krasovski Functional for stability analysis of time-delay systems is introduced in [72] .

• The article [31] proposes a convex optimization approach for the design of relay feedback controllers. Furthermore, the approach is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid of the order of the sampling interval.

• The paper [40] addresses the controller design problem for bilateral teleoperation over unreliable networks. The stability and tracking performance analysis are presented for a novel force-reflecting emulator control scheme.

• The problem of time optimal control design is considered for a chain of integrators in [74] . The suboptimal continuous ILF-based solution is presented and compared with the optimal discontinuous feedback.

• In the erratum [26] recently proposed conditions on finite-time stability in time-delay systems are revisited and it is shown that they are incorrect. General comments on possibility of finite-time convergence in time-delay systems and a necessary condition are given.

• The problem of formulation of an equivalent characterization for instability is considered in [56] . The necessary part of the Chetaev's theorem on instability is formulated. Using the developed necessary instability conditions, the Anti-control Lyapunov Function (ALF) framework is extended and the Control Chetaev Function (CCF) concept is proposed as a counterpart of the Control Lyapunov function (CLF) theory.

• The paper [25] extends the notion of oscillations in the sense of Yakubovich to hybrid dynamics. Several sufficient stability and instability conditions for a forward invariant set are presented. The consideration is illustrated by analysis of a model of two-link compass-gait biped robot.

• The paper [15] deals with the design of an active fault-tolerant control strategy based on the supervisory control approach technique for linear time invariant MIMO systems affected by disturbances, measurement noise, and faults.

• The problem of phase regulation for a population of oscillating systems is considered in [21] . The proposed control strategy is based on a Phase Response Curve (PRC) model of an oscillator.

• The paper [51] deals with the design of an estimator-based supervisory Fault Tolerant Control scheme for Linear Time Invariant systems. A formal stability proof based on dwell-time conditions is established.

• In [39] , we propose a general statistical framework for model based compressive sensing, where both sparsity and structure priors are considered simultaneously. It is based on the Latent Variable Analysis and the Gamma-Gaussian modelling.

• The paper [64] investigates the left invertibility for nonlinear time delay system with internal dynamics under some assumptions imposed on the internal dynamics. Causal and non causal estimation of the unknown inputs are respectively discussed, and the high-order sliding mode observer is used to estimate the observable states.

• In the paper [54] a simple second order model is proposed for modeling the pressure dynamics with a pure time delay on the control input. The Artstein transformation is applied in order to design the stabilizing robust nonlinear controller.