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The Lyapunov stability theorem has been proposed for more than 100 years, and it is still one of the most important theories in control science and other fields. In this paper, a new stability theorem (Extended Lyapunov stability theorem) is proposed and proved to be different from Lyapunov stability theorem. The Lyapunov stability theorem demands that the time derivative of Lyapunov function is negative...
This paper aims to understand the stability domain of a missile target system modeled under the TPN (true proportional navigation) guidance laws and to give suitable and useful methods to achieve stability by varying certain parameters in the system. We have used Laplace method to convert the nonlinear equations of motions into the frequency domain in order to find its stability. A Bode plot of the...
This paper deals with Takagi-Sugeno (T-S) systems stabilization based on a static output feedback (SOF) non-PDC control law. To investigate SOF stabilization, the closed loop dynamics is written using a descriptor redundancy formulation. This approach allows avoiding appearance of crossing terms between the controller's and the T-S system's matrices. Thus, based on a fuzzy Lyapunov candidate function...
This paper addresses a problem of finding an optimal dynamic quantizer for nonlinear control subject to discrete-valued signal constraints. The quantizers to be studied are in the form of a nonlinear difference equation and are evaluated by the performance index expressing the difference between the resulting quantized system and the usual (unquantized) system. To solve the problem, we first derive...
We characterize the stability and achievable performance of networked estimation under correlated packet losses described by the Gilbert-Elliot model. For scalar continuous-time linear systems, we derive closed-form expressions for the mean-square distortion of the optimal estimator. The conditions for stable mean square estimation error are equivalent to those obtained previously for stability of...
This paper presents an adaptive observer design for nonlinear systems that have parametric uncertainties in the unmeasured state dynamics. Without persistency of excitation (PE) the convergence of the state estimation error to zero is proved. Under PE conditions, uniform global asymptotic stability of the origin of the state and parameter error is shown. Furthermore, if the regressor is sufficiently...
Interconnection of several hybrid input-to-state stable (ISS) systems is considered in this paper. We ask under what condition is such an interconnection stable and how an ISS-Lyapunov function can be constructed for the whole interconnection. Small-gain condition to assure stability is given. A construction of an ISS-Lyapunov function for the whole system is provided under the small-gain condition.
Necessary and sufficient stability conditions are given for the existence of a continuous Lyapunov function for a semicontinuous, stochastic discrete-time system. The continuity of the Lyapunov function is linked to robustness of the stability property, which reduces to classical stability plus convergence for deterministic systems. The nature of the Lyapunov results are inspired by Lyapunov results...
Acting as a supervision or optimization module for a local controller, indirect iterative learning control (ILC) can improve closed-loop performance along the batch direction. In particular, if the set-point for the local controller is updated, this type of indirect ILC is termed set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance; however, there is no reported work...
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...
This paper is concerned with the stochastic stabilizability problem of time-delayed Markovian jump bilinear systems with saturating actuators. Based on the reduction method, sufficient conditions are proposed to guarantee local exponential stochastic stability of the closed-loop systems with delayed feedback control. A numerical example is provided to demonstrate the effectiveness of the proposed...
In this paper, we propose a decentralized adaptive output-feedback controller for a class of large-scale time-delay nonlinear systems with unknown high-frequency-gain signs. We establish global asymptotic stabilization results, without using Razumikhin Theorem or constructing Lyapunov-Krasovskii functionals. The paper enlarges the class of large-scale nonlinear systems for which global decentralized...
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...
A Smith Predictor-like design for compensation of arbitrarily long input delays is available for general, controllable, possibly unstable LTI finite-dimensional systems. Such a design has not been proposed previously for problems where the plant is a PDE. We present a design and stability analysis for a prototype problem, where the plant is a reaction-diffusion (parabolic) PDE, with boundary control...
This paper studies the ISS (input-to-state stability) for a class of HDS (hybrid dynamical systems). By using the concept of hybrid time for HDS, two kinds of ISS notions are proposed. They are called the first ISS property and the second ISS property of HDS. By employing the ISS properties on continuous and/or discrete dynamics in the HDS, the first and second ISS properties for the whole HDS are...
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...
A framework for addressing a potential instability problem in adaptive control and iterative identification and controller design algorithms is proposed. Suppose an unknown plant is stabilized by a known controller, some knowledge of this stable closed-loop system is available, and the use of a new controller to replace the current stabilizing controller becomes imminent. Our analysis results assume...
In this paper, we present some new results on frequency weighted balanced truncation which is a significant improvement on Lin and Chiu's frequency weighted balanced truncation technique. The reduced order models which are guaranteed to be stable in case of double-sided weighting, are obtained by direct truncation. Two sets of simple, elegant and easily calculatable a priori error bounds are also...
This paper investigates string stability issues in homogeneous strings of strictly proper feedback control systems with unidirectional nearest neighbour communications, using only linear systems with two integrators in the loop. We show under which conditions the induced L2-norm of the disturbance to error transfer function is bounded independently of the string length when using a constant time headway...
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