Systems & Control Letters最新文献

In this paper, by using the concept of Yosida distance between two closed linear operators, we study the stability radius $r\left(A\right)$ of linear systems $u^{\prime }\left(t\right)=Au\left(t\right)$, where $A$ is the generator of an analytic semigroup, under unbounded perturbations in this class of generators. We show that $r\left(A\right)=1/{sup}_{s\in R}{\Vert R(is,A)\Vert }_{L\left(X\right)}$, so extending a classic result by Henrichsen and Pritchard to the infinite-dimensional case. A formula of the dichotomy radius is also established. Finally we give an estimate of the stability radius of general $C_0$-semigroups. Two examples from a parabolic equation are given.

In this paper, we are concerned with the regional exponential stabilization of a 1-D Burgers’ equation under non-local/Neumann actuation and boundary measurement via a modal decomposition method. For non-local actuation, we suggest two control strategies: continuous-time control, and delayed sampled-data control implemented by zero-order hold (ZOH) device, both relying on finite-dimensional observer. For boundary actuation, we employ dynamic extension and consider an observer-based delayed sampled-data controller implemented by generalized hold device. For both cases, we suggest a direct Lyapunov method for the $H^1$-stability of the full-order closed-loop system. We provide efficient linear matrix inequality (LMI) conditions for finding the observer dimension, as well as upper bounds on the domain of attraction, sampling intervals and delays, that preserve the exponential stability. We prove that for some fixed upper bounds on the initial values and sampling intervals, the feasibility of LMIs for some $N$ (dimension of the observer) implies their feasibility for $N+1$. Numerical examples illustrate the efficiency of the proposed method.

This paper investigates the estimation problem of a class of nonlinear Markov jump systems with actuator and sensor faults. The main goal is to design a distributed fault-tolerant observer to estimate system states and actuator faults simultaneously. Firstly, a novel distributed observer network is constructed to compensate the missing information of unobservable nodes of the system. Next, a class of new redundant sensors are set up on each distributed observer node to obtain more output measurement samples. More importantly, when some of the mentioned sensors occur faults, an index of sensor heath level is constructed to characterize the quality of the faulty sensor information. Further, a novel algorithm is designed to mask low quality output information and filter out relatively healthy one automatically. Based on the selected healthy output information, the system state and actuator fault are estimated in the case of sensor failure. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

A chaotic system $X_{n+1}=F\left(X_n\right)$ in certain cases can be stabilized with taking a weighted average of the state variable and the next-stage position $X_{n+1}=U{X}_n+(I-U)F\left(X_n\right)$ corresponding to a modified Prediction-Based Control with a diagonal non-scalar matrix $U$ ensuring stability of the controlled system. Sharp constants are determined for the values on the diagonal providing local stabilization. Introducing small additive noise in the control parameters keeps convergence of all solutions to the equilibrium. As noise increases, we distinguish between the cases when noise can stabilize the system while control with mean parameters does not, and those when noise destabilizes. Noise bounds allowing to lower average control intensity are determined. In the case of real eigenvalues of the Jacobian matrix being less than −1, these conditions are universal, while for complex eigenvalues, they are sharp.