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In this paper we study the properties of existing non-parametric methods for estimating the plant and noise transfer functions of a linear dynamic system. The analysis is based on the recent insight that leakage errors in the frequency domain have a smooth nature that is completely similar to the initial transients in the time domain. This not only allows us to understand better the existing classic...
This paper collects a number of recent results on stability and L2 gain of switched linear systems (both deterministic and stochastic) under a dwell time constraint. The switching signal orchestrates the commutations between linear systems (in the deterministic case) or Markov jump linear systems (in the stochastic case). In the latter case, the switching affects both the dynamics of the underlying...
This paper establishes conditions for the existence of optimal stationary policies for the long-run average cost control problem of linear stochastic systems. The control takes a general structure in such a manner that it contains, as particular case, a large number of linear control problems. The main contribution of this paper is to show that if (i) the system is controllable to the origin and (ii)...
This note considers the long-run average cost control problem of a discrete-time stochastic system. The stochastic system is assumed to be linear with respect to the state but the controls possess a general structure, possibly nonlinear. The main contribution of this paper is to show the existence of an optimal stationary policy for the long-run average cost problem provided that (i) there exists...
Linear, state delayed, continuous-time systems are considered with both stochastic and norm-bounded deterministic uncertainties in the state-space model. The problem of robust dynamic H∞ output-feedback control is solved, for the stationary case, via the input-output approach where the system is replaced by a nonretarded system with additional deterministic norm-bounded uncertainties. In this problem,...
Range only tracking problems arise in extended data collection for inverse synthetic radar applications, robotics, navigation and other areas. For such problems, the conditional density of the state variable given the measurement history is multi-modal or exhibits curvature, even in seemingly benign scenarios. For this reason, the use of extended Kalman filter (EKF) and other nonlinear filtering techniques...
Optimal communication/control analysis and design of dynamical controlled systems, when there are finite capacity communication constraints often involve information and control theoretic analysis. This paper, employees information theoretic concepts, which are subject to causality, and thus applicable to control/communication system analysis and design in which encoders, decoders and controllers...
The guaranteed cost control problem for stochastic multimodeling systems with norm bounded uncertainty is investigated. The main contribution in this paper is that a new parameter independent controller is derived by solving the reduced-order slow and fast stochastic algebraic Riccati equations (SAREs) whose dimension is smaller than the dimension of full-order stochastic multimodeling algebraic Riccati...
Estimating the domain of attraction of equilibrium points of nonlinear systems is an important problem in numerous fields. Recently, some methods based on LMIs have been developed for addressing this problem in the case of polynomial systems. This paper proposes an approach for extending the use of LMIs to the case of non-polynomial systems. In particular, it is shown how the estimate achievable with...
This paper provides a new method to estimate the Region of Asymptotic Stability (RAS) via computing the union of several regions, each one of them is known to be a subset of the RAS. The union is computed analytically by using R-functions, which represent a natural extension of Boolean functions to real-valued functions. The benefit of the proposed approach is that usually the best Lyapunov function...
In this paper we investigate the stability of discrete-time linear time-invariant systems subject to finite-level logarithmic quantized feedback. Both state feedback and output feedback are considered. We develop an LMI approach to estimate, for a given controller and a given finite-level quantizer, a set of admissible initial states and an associated attractor set in a neighborhood of the origin...
We propose a method to compute invariant subsets of the robust region-of-attraction for the asymptotically stable equilibrium points of systems with polynomial nominal vector fields and unmodeled dynamics. The effects of unmodeled dynamics are accounted for as systems satisfying certain gain relations or dissipation inequalities. The methodology is extended to systems with parametric uncertainties...
We study feedback interconnections of two nonlinear systems, that are asymptotically stable at a fixed point. It is shown that if the subsystems are input-to-state stable and the corresponding gains satisfy a small gain condition, then estimates for the domain of attraction of the whole system may be obtained by calculating robust Lyapunov functions for the subsystems. The latter task can be solved...
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