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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...
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 paper presents a method of designing a modified repetitive control system (MRCS) based on a two-dimensional (2D) continuous-discrete hybrid model. First, a 2D continuous-discrete hybrid model of MRCS is established. Next, the design of the feedback controller of the MRCS is converted to the stabilization problem of the 2D hybrid system with a static-state feedback. Then, by using a 2D Lyapunov...
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...
In this paper, we consider the model reference adaptive control (MRAC) problem of switched linear systems in which the parameters and switching time instants are all unknown. We apply the output feedback variable structure (VS) based adaptive controller to switched linear systems with general relative degrees and show error convergence and signal boundedness properties by multiple Lyapunov functions...
In this note, we investigate exponential mean-square stability for a class of time-delay Markovian jump linear systems with state-dependant switching. By solving a set of linear matrix inequalities (LMIs), a state-feedback nonlinear controller is obtained, which guarantees globally exponential stability of such systems in the mean-square sense. Based on this, an adaptive state-feedback control law...
In this paper, we show that adaptive control can be traded off against time-varying static state feedback (TVSSF) for a certain class of uncertain nonlinear systems. More precisely, we propose a systematic design procedure leading to TVSSF guaranteeing asymptotic (exponential) stability. Our approach, coined Direct time injection in the loop (DTIL), allows to remove the need for the integral action...
The paper studies semi-global practical input-to-state stability (SGP-ISS) of a parameterized family of discrete-time systems that may arise when an approximate discrete-time model of a sampled-data system with disturbances is used for controller design. It is shown under appropriate conditions that if the solutions of the time varying family of discrete-time systems with disturbances converge uniformly...
This paper deals with stabilization of networked control systems (NCS) affected by uncertain time-varying delays and data packet dropouts. We point out that such network effects are likely to render the classical control Lyapunov function (CLF) method unfeasible, mainly due to the monotonic decreasing condition. To solve this problem we make use of a discrete-time equivalent of a control Lyapunov-Razumikhin...
In this paper we study the characterization of asymptotic stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension...
In this paper we give conditions that a discrete time switched linear systems must satisfy if it is stable. We do this by calculating the mean and covariance of the set of matrices obtained by using all possible switches. The theory of switched linear systems has received considerable attention in the systems theory literature in the last two decades. However, for discrete time switched systems the...
This paper develops semistability analysis results for nonlinear switched systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. The main results of the paper involve sufficient conditions for semistability using multiple Lyapunov functions and integral-type inequalities.
We show that for a general class of distributed power control algorithms in wireless networks, if a feasible steady state power allocation exists, this is asymptotically stable for arbitrary gains and time varying heterogeneous delays. The analysis exploits certain contraction properties of the interference in such algorithms, and makes use of Lyapunov Razumikhin functions to address the infinite...
Previous inverse optimal adaptive controllers (IOACs) have been developed that can handle structured (i.e., linear in the parameters (LP)) uncertainty for a particular class of nonlinear systems. A full-state feedback IOAC is developed in the companion Part I paper for Euler-Lagrange systems with an uncertain time varying inertia matrix. In this paper, an output feedback IOAC is developed to asymptotically...
This paper addresses the robust stability and stabilization of continuous-time linear systems with Markov jump parameters taking values in a finite set. It is shown how each of the robust analysis and synthesis problems can be expressed in terms of two alternative linear matrix inequalities, in which the scaling parameters appear as decision variables. As a by-product, new contributions to the theory...
We study certain difference equations arising in the stability analysis of Kalman filtering for a class of linear, discrete-time, possibly non-detectable systems with incorrect noise information. We obtain bounds for the solutions of these equations and the Riccati difference equation associated with the Kalman filter, under the assumption that the Riccati solution is bounded above and an assumption...
This paper presents a new stability analysis of linear networked control systems. The new method is inspired by discontinuous Lyapunov functions that were introduced by using impulsive system representation of the sampled-data and of the networked control systems respectively. In the recent paper piecewise-continuous (in time) Lyapunov-Krasovskii functionals have been suggested for the stability analysis...
This paper investigates the global exponential stability of static neural networks (SNN) with time-varying delays and fixed moments of impulsive effect. Sufficient conditions for the exponential stability are established by using Lyapunov functions and the Razumikhin technique.
According to the characteristics of long time-delays, large inertia and time-variation in the dissolved oxygen control method of sewage treatment, one fuzzy-Smith control model on dissolved oxygen control is presented in this paper. This model has the merits of a high robustness in fuzzy controller and a compensation for time delay in Smith predictor. After simulation experiment, the result is shown...
This paper deals with a class of T-S fuzzy stochastic neural networks with uncertainty and time varying delays. A sufficient condition on asymptotical stability is developed in the LMI setting.
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