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This paper proposes a method to estimate the region of attraction of nonlinear polynomial systems. Based on quadratic Lyapunov functions, stability analysis conditions in a ??quasi??-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the Lyapunov matrix maximizing the estimate of the region of attraction of the origin.
The nonlinear robust stability theory of Georgiou and Smith (IEEE Trans. Auto. Control, 42(9):1200-1229, 1997) is generalized to the case of notions of stability with bias terms. An example from adaptive control illustrates non trivial robust stability certificates for systems which the previous unbiased theory could not establish a non-zero robust stability margin. This treatment also shows that...
We present an approach for compensating input delay of arbitrary length in nonlinear control systems. This approach, which due to the infinite dimensionality of the actuator dynamics and due to the nonlinear character of the plant results in a nonlinear feedback operator, is essentially a nonlinear version of the Smith Predictor and its various predictor-based modifications for linear plants. Global...
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...
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.
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...
Following the procedure used by Kamke, on the basis of the concepts of symmetry and orbital symmetry introduced by S. Lie, aim of this paper is to extend such a reasoning to classify systems for which the semi-invariants can be computed in closed-form, whence possibly used for the computation of Lyapunov functions as well. The concept of semi-invariant extends both the concept of first integral (a...
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...
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...
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...
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...
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...
We consider networks of input-to-state dynamically stable (ISDS) systems and provide a small gain condition under which the entire network is again ISDS. A Lyapunov formulation of the nonlinear small gain theorem for two interconnected ISDS systems is proved. It provides a constructive method to find an ISDS Lyapunov function for such an interconnection.
The robustness of quantized continuous-time non-linear systems with respect to the discrepancy (mismatch) between the ranges of the encoder and the decoder quantizers is investigated. A condition which guarantees asymptotic stability and which describes the interplay between quantization density and mismatch is derived.
A new small-gain theorem is presented for general nonlinear control systems described either by ordinary differential equations or by retarded functional differential equations. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability results. It is shown that the proposed approach recovers several recent results as...
The control of a new kind of airship is presented. By restricting its flight to a vertical plane, the mathematical model is reduced. The simplified model is proved to be minimum phase, and a nonlinear controller based on input-output linearization is designed. Since the performance of the controller is significantly impacted by the choice of parameters, simulations of three different pole placement...
This paper is concerned with the problem of receding horizon control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a nonlinear feedback policy with respect to noise measurements and show that the resulting mathematical program has a tractable convex solution. Moreover, under the assumption that the zero-input...
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.
A full-order sliding-mode state observer for a class of nonlinear continuous-time dynamic systems is proposed and conditions for the stability of the estimation error in the absence of noises are provided. If the system is affected by bounded disturbances, under such conditions the existence of an attractive invariant set for the estimation error is ensured. The design of the observer can be made...
A new fractional-order chaotic system, fractional-order Lorenz-Stenflo (LS) system, is found in this paper. Chaos can exist in the fractional-order LS system with order as low as 3.6. The chaotic dynamics of this system is investigated. Then based on Laplace transformation theory, the controller of complete synchronization is designed for this system. Moreover using stability theory of linear fractional-order...
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