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Variation paradigm is introduced for stability in terms of asymptotic gain of persistent dwell-time switched time-delay systems. The principle of small-variation small-state is conceived to formulate conditions on ultimate variations between end times of dwell-time switching intervals for convergence in these intervals. Trajectory convergence is then derived using evolutionary data in both retarded...
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.
We consider a plant switching among a set of dynamic systems each associated with a single stable equilibrium point. We assume that a constraint region for the state is assigned. The main problem is that of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the absence of state measurements. We introduce the concepts of modal and transition dwell...
This paper discusses the dynamical servo control problem for the Acrobot - a mechanics with two links while just one actuator applied to the second link. The dynamical servo control aims to access generic points in the state space not just the equilibrium points. Stabilizing of generic points is impossible and a possible way is to stabilize some periodic orbits passing through the desired points....
This paper develops semistability and uniform semistability analysis results for switched linear systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. Since solutions to switched systems are a function of the system initial conditions as well as the switching signals, uniformity...
In this paper we consider the problem of designing a multi-controller K that consists of a family of stabilizing controllers {Km}m=1n, where each controller Km belongs to a constrained set Km. Our goal is to determine the controllers {Km}m=1n (and an associated switching trajectory if switching is controllable) to optimize the closed-loop system performance. Based on a special implementation of...
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.
In this paper, the design of variable structure control (VSC) for uncertain discrete systems with time-delays is considered. The original uncertain discrete system with time-delay is simplified to uncertain discrete system without time-delay. Using exponential reaching law, the reason of causing uncertain discrete system without time-delay chattering is given, and using boundary layer, an improved...
In this paper a hybrid control for buck converters is proposed that is able to guarantee voltage tracking and maximum voltage and current ripple simultaneously. The controller is based on the piece-wise model of the converter and it works by switching on or off once a set of performance surfaces is reached. The controller provides global attractiveness and asymptotic stability to a bounded set.
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...
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