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This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poincare??-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability...
In this paper, we study the dynamics of a viral spreading process in random geometric graphs (RGG). The spreading of the viral process we consider in this paper is closely related with the eigenvalues of the adjacency matrix of the graph. We deduce new explicit expressions for all the moments of the eigenvalue distribution of the adjacency matrix as a function of the spatial density of nodes and the...
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...
We are concerned with parameter estimation and stabilization of a one-dimensional wave equation with unknown constant signal disturbance suffered from boundary observation at one end and the non-collocated control at another end. An adaptive observer is designed in terms of measured velocity with unknown constant disturbance. The backstepping method is adopted in design of the feedback law. It is...
A new adaptive inventory control strategy is developed by applying online adaptation in the framework of passivity-based control. Given the definition of inventory, a feedback-feedforward control structure is derived from the passivity theory. The stability analysis is also given in this paper. This control strategy is demonstrated in simulations and an application on a pressure tank system.
Linear Matrix Inequalities (LMIs) provide a powerful analysis and synthesis framework for linear systems. In this paper, we use LMIs to develop positive observers for positive linear discrete-time (PLDT) systems with both parameter uncertainties and time delay. Specifically, we first present some equivalent conditions for the asymptotic stability of positive linear discrete-time delay systems, which...
This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensional system is obtained. At each step of the reduction process, a quotient is taken along one-dimensional integral manifolds of the input vector field...
A computational method for stability analysis of discrete-time piecewise linear systems is presented. The method is based on combining the solutions to two separate problems: one is to obtain stabilizing switching sequences between linear dynamics, and the other is to obtain an increasing sequence of state-space partitions. Examples show that there are cases where the presented method is very useful.
This paper studies the stabilization problem for a class of networked control systems (NCSs) with communication constraints and random packet dropouts. The considered plant is equipped with multiple sensor nodes and actuator nodes. Only one of them can communicate with the controller at each transmission instant due to the communication constraints, and packet dropouts may occur at each transmission...
In this paper, adaptive control is presented for a class of parametric output feedback nonlinear systems with output constraint. Adaptive observer backstepping is adopted to achieve the output tracking. To prevent the output constraint violation, the barrier Lyapunov function (BLF) is employed in Lyapunov synthesis. By ensuring the boundedness of the BLF, we also guarantee that the output constraint...
This paper studies a non-linear, discrete-time, matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behaviour. The problem of partial stability, which requires that a specific component of the state of the system converges exponentially, is studied and solved. The convergent state...
It is mainly discussed Lasalle's invariant principle for a class of nonlinear systems with discontinuous righthand sides on the basis of vector Lyapunov function in the framework of Filippov solutions. Assuming that the system is Lebesgue measurable and non-Lipschitz continuous, we extend Lasalle's invariant principle for a class of discontinuous dynamical systems by means of Filippov solutions and...
This paper presents a sum of squares (SOS, for brevity) approach to polynomial fuzzy observer design for polynomial fuzzy systems. First, we briefly summarize previous results with respect to a polynomial fuzzy system and controller that are more general representation of the well-known Takagi-Sugeno (T-S) fuzzy system and controller, respectively. Secondly, we propose a polynomial fuzzy observer...
This paper deals with tracking performance of linear time-invariant discrete time SISO systems. In the existing results, the fundamental limitations are analyzed based on the knowledge of reference signals such as the step, the trigonometrical signals and so on. Our purpose is to find the closed form expressions of the tracking performance limitation for the general class of reference inputs. Moreover,...
Smith Predictor-like designs for compensation of arbitrarily long input delays are commonly available only for finite-dimensional systems. Only very few examples exist where such compensation has been achieved for PDE systems, including our recent result for a parabolic (reaction-diffusion) PDE. In this paper we address a more challenging wave PDE problem, where the difficulty is amplified by allowing...
In our recent work, an efficient nonlinear system identification approach using wavelet based State Dependent Parameter (WSDP) models has been proposed and investigated. This model has some unique properties which are very useful for the investigation of its bounded characteristics. This paper presents results on the bounded characteristics of WSDP models. These results reveal the clear relationship...
This paper proposes novel stability conditions of nonlinear systems in Takagi-Sugeno's form. This problem has been studied over twenty years with many sufficient conditions. Recently, asymptotically necessary and sufficient conditions are obtained, which are preferred with respect to common quadratic Lyapunov function. This paper considers general forms of homogeneously polynomially nonquadratic Lyapunov...
This paper is concerned with stability analysis of discrete-time networked control systems in the case where both input and output channels are characterized by a multiple-packet transmission policy. A necessary and sufficient condition for stability is obtained for known packet dropping probabilities. The issue of stability robustness of a system against packet dropping is discussed and addressed...
This paper addresses the H?? stability analysis of neutral time-delay systems with multiple commensurate delays including those with poles asymptotic to the imaginary axis. This extends previous work where only the single delay case was considered. Some frequency-domain tests for this kind of stability are proposed.
This paper provides synchronization conditions for networks of nonlinear systems, where each component of the network itself consists of subsystems represented as operators in the extended L2 space. The synchronization conditions are provided by combining the input-output properties of the subsystems with information about the structure of network. The work is motivated by cellular networks where...
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