This paper studies a class of impulsive switched systems with persistent bounded disturbance using robust attractor analysis and multiple Lyapunov functions. Some sufficient conditions for internal stability of the systems are obtained in terms of linear matrix inequalities (LMI). Based on the results, a simple approach for the design of a feedback controller is presented to achieve a desired level of disturbance attenuation. Numerical examples are also worked out to illustrate the obtained results.

This paper deals with the optimal tracking problem for switched systems, where the control input, the switching times and the switching index are all design variables. We propose a three-stage method for solving this problem. First, we fix the switching times and switching index sequence, which leads to a linear tracking problem, except different subsystems are defined in their respective time intervals. The optimal control and the corresponding cost function obtained depend on the switching signal. This gives rise to an optimal parameter selection problem for which the switching instants and the switching index are to be chosen optimally. In the second stage, the switching index is fixed. A reverse time transformation followed by a time scaling transform are introduced to convert this subproblem into an equivalent standard optimal parameter selection problem. The gradient formula of the cost function is derived. Then the discrete filled function is used in the third stage to search for the optimal switching index. On this basis, a computational method, which combines a gradient-based method, a local search algorithm and a filled function method, is developed for solving this problem. A numerical exampleis solved, showing the effectiveness of the proposed approach.

This paper presents a continuous wall-following controller for wheeled mobile robots based on odometry and distance information. The reference for this controller is the desired distance from the robot to the wall and allows the robot to follow straight wall contour as well as smoothly varying wall contours by including the curvature of the wall into the controller. The asymptotic stability of the control system is proved using a Lyapunov analysis. The controller is designed so as to avoid saturation of the angular velocity command to the robot. A novel switching scheme is also proposed that allows the robot to follow discontinuous contours allowing the robotic system to deal with typical problems of continuous wall-following controllers such as open corners and possible collisions. This strategy overcomes these instances by switching between dedicated behavior-based controllers. The stability of the switching control system is discussed by considering Lyapunov concepts. The proposed control systems are verified experimentally in laboratory and office environments to show the feasibility and good performance of the control algorithms.

In this paper, we solve an optimal control problem using thecalculus of variation. The system under consideration is aswitched autonomous delay system that undergoes jumps at theswitching times. The control variables are the instants when theswitches occur, and a set of scalars which determine the jumpamplitudes. Optimality conditions involving analytic expressionsfor the partial derivatives of a given cost function with respectto the control variables are derived using the calculus ofvariation. A locally optimal impulsive control strategy can thenbe found using a numerical gradient descent algorithm.