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In this paper, we consider full order modeling, i.e., when the true system belongs to the model set. We investigate the minimum amount of input energy required to estimate a given linear system with a full order model within a prescribed degree of accuracy γ, as a function of the model complexity. This quantity we define to be the “cost of complexity.” The degree of accuracy is measured by the inverse...
Practical stabilizability of discrete-time (DT) switched systems is studied in this paper. We first prove a sufficient condition for ??-practical asymptotic stabilizability of DT switched systems, then we focus on switched affine systems and present an approach to estimating the minimum bound for practical stabilizability. Based on the approach, we present several new sufficient conditions for global...
This paper proposes a novel stability analysis of linear systems with sampled-data inputs. Inspired by the input-delay approach and the stability of impulsive systems, this method provides novel sufficient stability conditions. The stability analysis concerns both constant and time-varying sampling periods. The delay-dependent conditions are expressed using computable linear matrix inequalities. Several...
This paper provides a Lyapunov formulation of the cyclic-small-gain theorem for general dynamical networks (large-scale systems) composed of interconnected input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying cyclic-small-gain are constructed from the ISS-Lyapunov functions of the subsystems.
For LTI systems with a time-varying input delay, an explicit formula for predictor feedback was presented by Nihtila in 1991. In this note we construct a time-varying Lyapunov functional for the closed-loop system and establish exponential stability. The key challenge is the selection of a state for a transport PDE, which has a non-constant propagation speed, and which is the basis of the stability...
This letter introduces a strategy design of sliding mode control (SMC) for two-dimensional (2-D) systems. The dynamic updating of the 2-D system is considered as a Roesser model (RM). The proposed method consists of two stages, switching surface design and control law design. Moreover, the robustness of the proposed method for an uncertain system has been investigated. Simulation results verify the...
This paper is concerned with the stability analysis of discrete-time systems with time-varying state delay. By defining a new Lyapunov functional and by making use of novel techniques to achieve delay dependence, a new criterion is obtained for the asymptotic stability of these systems. The proposed criterion is less conservative as well as needs fewer decision variables than some pervious ones, which...
This paper addresses an Euler-Bernoulli beam equation under boundary control and collocated observation for which observation suffers a constant time delay. Since this system is well-posed in the sense of D.Salamon, exactly observable and controllable, we construct an infinite-dimensional observer which results in a well-posed observer system. After designing estimated state feedback control we show...
Variation paradigm is introduced for stability in terms of asymptotic gain of persistent dwell-time switched time-delay systems. The principle of small-variation small-state is conceived to formulate conditions on ultimate variations between end times of dwell-time switching intervals for convergence in these intervals. Trajectory convergence is then derived using evolutionary data in both retarded...
In practice, there exist such controlled systems in which some states are often not available, not measurable or too expensive to measure. For such systems, impulsive control inputs may be exerted on the available partial states so as to stabilize the underlying systems. This paper is concerned with analyzing the stability of a class of nonlinear time-delay systems with partial states subject to impulsive...
We investigate control of the state of infection dynamics without explicit modeling of the immune system. By using constant drug dosage we prove almost global asymptotic stability of an equilibrium with assumption of zero immune system, and then by varying the drug effect we study how to drive any initial state into a region which represents desirable clinical conditions. These results can be used...
We introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer...
In this paper, a robust stabilization of the uncertain singularly perturbed system via a networked state feedback with the transmission time-delay is addressed. Taking its nominal system as a model plant, propagation unit and overall states chosen to overcome the difficulty of communication delay, the characterization of singular perturbation for the overall hybrid system is still preserved on each...
This paper considers interval time-varying delay systems with delayed estimation of the delay. This case is often encountered in the Networked Control Systems (NCS) field. Based on Lyapunov-Krasovskii functional methods and linear matrix inequality (LMI) techniques, a switching state feedback controller is designed to guarantee the exponential stability. The controller switches according to the measured...
This paper concerns the problem of swinging up multiple parallel pendulums on a cart by controlling only the energy of pendulums. Although the analysis of the energy control for swinging up single pendulum and two pendulums on the cart has been achieved in existing literature, a few analysis results have been reported for the case of multiple (greater than 2) pendulums. In this paper, we aim to provide...
This article is concerned with the asymptotic stability of a class of nabla dynamic equations on time scales. By the use of Lyapunov direct method on time scales, some criteria on stability of the first-order linear dynamic equations are obtained, which extend the present results. The cobweb model is illustrated in the end.
This paper takes the condition that individuals in eclipse period could translate into infective individuals or recovered at a certain probability, and propose a new SEIRS model on the basis of normal SEIRS model. First of all, it analyzes the spread of the disease using the mean field theory and obtains a theoretical critical threshold. From analysis the global behavior of the model is entirely determined...
This paper is concerned with the stabilization of networked control systems with nonlinear perturbations and fast-varying network-induces time-delay, and data dropout is also taken into consideration. Using LMI approach, new criteria are proposed for the controller design. The new criteria are irrelevant to the bound of the derivative of the delay, no constrain is imposed to the matrix structure....
We consider the averaging method for stability of rapidly switching nonlinear and linear systems with disturbances. First, we show that the input-to-state stability (ISS) analysis results for continuous-time systems in apply directly to nonlinear rapidly switched systems that we consider. We show that the notions of strong and weak averages that were proposed in play an important role in the context...
A new type of global stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability of the compact set composed by all invariant solutions of a nonlinear system (several equilibriums, for instance) is analyzed. Consideration of such set allows us to present global stability properties for multi-stable systems.
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