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In this paper we present a systematic procedure to design robust fuzzy controller for exponentially stabilizing affine nonlinear systems, based on their TS fuzzy model. For robust design we consider modeling error in TS model and as well as perturbation in the original nonlinear system. Minimization of cost function along with mapping closed loop poles to desired poles are considered simultaneously...
This paper presents linear matrix inequalities for stability analysis for networked control systems (NCSs) that incorporates various network phenomena: time-varying sampling intervals, packet dropouts and time-varying delays that may be both smaller and larger than the sampling interval. The problem is approached from a discrete-time modelling perspective. A comparison is made between the use of parameter...
This article studies robust stability of affine fuzzy systems in the framework of input-to-state stability (ISS) using piecewise ISS Lyapunov function by which additive disturbance inputs are explicitly taken into account in the synthesis procedures. The sufficient conditions for ISS of affine fuzzy systems are expressed in terms of bilinear matrix inequalities (BMIs), and further converted to LMIs...
An adaptive fuzzy controller for controlling a multi-input-multi-output uncertain nonlinear system is proposed in this paper. The controller design is observer based since not all the system states are measurable. The fuzzy adaptive controller with modulated membership function (FAC_MMF) modulates the fuzzy sets on both the consequent and antecedent parts by adjusting a few parameters. As searching...
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.
This paper introduces the chaos synchronization between two different hyperchaotic systems with fully unknown parameters, i. e. the synchronization between hyperchaotic Lorenz system and hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived for the case when the parameters of the drive and response systems to be synchronized are fully uncertain. Finally,...
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 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...
We establish a unified approach to stability and L2 gain analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for stability of all subsystems, then the...
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...
The exothermic continuous stirred tank reactor (CSTR) is a classical yet complex case study of nonlinear dynamical systems. Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. In this paper we apply the power-shaping control approach to the exothermic CSTR study case. A global Lyapunov function is derived for the open-loop exothermic...
In this paper we revisit the contractive model predictive control framework and propose a new contractive constraint, which depending on selected candidate Lyapunov function and contracting factor can guarantee different types of system's stability. Simulation results are presented to illustrate the effect of the proposed contractive scheme.
In this paper a new Fuzzy/Kalman navigation system for Unmanned Aerial Vehicles (UAV) is presented. A closed loop velocity Fuzzy navigation system is proposed for stabilizing the UAV in a reference trajectory generated dynamically and for obtaining a forward velocity command. The Kalman's filter (KF) is included in the feedback line of the fuzzy control system to filter the internal noise of the sensors...
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, stability of delay discrete impulsive systems in which the state variables on the impulses are related to the time delay is investigated. And a number of stability criteria are obtained by using Lyapunov functions and Razumikhin technique. Two examples are also presented to illustrate the efficiency of the obtained results.
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.
This paper is concerned with the H∞ dynamic output feedback (DOF) control problem for continuous-time switched stochastic systems. By applying the average dwell time method and the piecewise Lyapunov function technique, a sufficient condition is first proposed, which guarantees the closed-loop switched stochastic system to be mean-square exponentially stable with a weighted H∞ performance. The H∞...
The cerebral cortex is a brain region that is implicated in complex behaviors. Understanding the dynamics of neurons in areas of the cerebral cortex is, thus, an important goal in neuroscience. Methods for recording the activity of populations of neurons in cortical areas are now becoming available, but there are few analytic methods available to analyze such data. This paper introduces a simple dynamical...
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.
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