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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.
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 investigates an event condition for event-driven controllers based on Lyapunov functions. Considering that constant values of a Lyapunov function define contour curves that form closed regions around the equilibrium point, in this paper we present a sampling mechanism that enforces job executions (sampling, control algorithm computation and actuation) each time the system trajectory reaches...
This paper considers networks consisting of integral input-to-state stable (iISS) subsystems and addresses the problem of verifying iISS property of a given network. First, we focus on construction of continuously differentiable Lyapunov functions, and derive a condition ensuring the iISS of the network comprising n subsystems. Although this approach referred to as the sum-type construction has not...
We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. In the first part of the paper, we characterize the buffer overflow exponents and the likeliest overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals...
This paper considers an M-member "individual-based" continuous time swarm model with individuals moving with a nutrient profile (or an attractant/repellent) in an n- dimensional space. It is proved that the swarm members aggregate and eventually form a cohesive cluster of finite size for Gaussian Profiles. Moreover, all the swarm members will converge to more favorable areas of the Gaussian...
A new stability condition in terms of LMIs is studied in this paper. Based on a premise-dependent Lyapunov function and multiconvexity, we release the conservatism that commonly exists in the common P approach. Comparison studies for common P and non-common P methods are demonstrated, showing relaxation is achieved via the proposed approach.
We compare the dynamic behavior of two CNN models: the original Chua-Yang model using the piecewise linear function and the hyperbolic model using the hyperbolic tangent. It is shown that, this two models are not topologically equivalent because in some parameter regions they exhibit a different number of equilibrium points.
New chattering-free feedback design for a class of perturbed nonlinear systems is presented. The idea is basically founded on uniting rational-power feedbacks with rational-type feedbacks that approximate the sign function. We show that the degree of smoothness of the applied controller depends essentially upon the number of the rational-power terms used in the expansion of the whole feedback. A detailed...
The phenomenon of long term instability of iterative learning control systems is examined. The concept of stability with respect to a specified trajectory is used to define a nonlinear biased gap metric. The resulting robust stability theorem, applied in a 2D setting, is used to prove the robust stability of a set of ILC algorithms engaged in trajectory tracking. The robust stability guarantee is...
We consider network resource allocation problems based on convex optimization, and their decentralized solutions by means of primal, dual, or primal-dual subgradient control. We show how Krasovskii's method, that seeks Lyapunov functions which are quadratic forms of the vector field, provides new global stability proofs for various problems of this kind. Applications include congestion control, cross-layer...
In a recent paper we presented the first adaptive control design for an ODE system with a possibly large actuator delay of unknown length. We achieved global stability under full state feedback. In this paper we generalize the design to the situation where, besides the unknown delay value, the ODE also has unknown parameters, and where trajectory tracking (rather than equilibrium regulation) is pursued.
This paper considers the problem of controlling a group of microrobots that can move at different speeds but that must all move in the same direction. To simplify this problem, the movement direction is made a periodic function of time. Although the resulting control policy is suboptimal for an infinite-horizon quadratic cost, a bound is provided on how suboptimal it is. This bound is extended to...
This paper presents the formulation of a Lyapunov function for an exponentially stable linear time-varying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear...
Two methods of the first Lyapunov exponent estimation for nonchaotic systems using time series are developed. Method's adequacy was tested on the typical systems. Analysis of the dependence between the estimation precision and the algorithm's parameters was performed.
This paper is concerned with robust passivity analysis of a class of uncertain nonlinear singular time-delay systems as well as with passivity-based sliding mode control of such systems. First we derive a delay-dependent sufficient condition expressed by means of linear matrix inequalities for achieving the generalized quadratic stability and robust passivity of the sliding mode dynamics. Then we...
This paper considers an M-member "individual-based" continuous time swarm model with individuals that moving with a nutrient profile (or an attractant/repellent) in an n-dimensional space. The swarm behavior is a result of a balance between inter-individual interplays as well as the interplays of the swarm agents with their environment. It is proved that the swarm members aggregate and eventually...
Compared with input-to-state (ISS) stability in global version, the concept of locally input-to-state (LISS) stability is more relevant and meaningful in practice. However, the local property raises difficulties in estimating the local region, which is seldom seen in literature. It is the aim of this paper is to investigate local regions of initial states and external inputs for the given system....
Presents two reaching laws of sliding mode for discrete-time variable structure control systems to solve the problem in designing the system control input. Considering the system control input is restricted, the reaching laws proposed in this paper adopt the approach angle and the distance to the sliding surface to regulate the system control input properly. By applying the proposed reaching laws...
This paper presents sufficient conditions for a perturbed trajectory to approach the desired trajectory as t approaches infinity. The sufficient condition guarantee that an upper bound decays exponentially
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