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In Part I of this paper, we introduced the notion of L??-vanishment and established several kinds of characterizations of this notion. Based on this notion, L?? low gain feedback was reconsidered and a systematic approach to L?? low gain feedback design was proposed. In this second part of the paper, we consider the parallel notion of L2-vanishment. We establish several characterizations of the L2...
We consider control systems of the type x?? = Ax+??(t)ub, where u ?? R, (A; b) is a controllable pair and ?? is an unknown time-varying signal with values in [0; 1] satisfying a permanent excitation condition of the kind ??t+Tt ?? ?? ??for 0 < ?? ?? T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T; ??) if the real part of the...
We consider the use of dynamic output feedback control to improve the transient response to a step input, for invertible multivariable systems. A method is given for designing a linear time-invariant output feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions.
The symmetric control systems have some interesting properties. This paper studies a class of symmetric system consists of a collocated second-order plant and a static output feedback controller. For the system, it is known that the internal stability and the robustness of the closed-loop system are guaranteed based only on the non-parametric structure condition. Our objective is to propose an optimal...
A limiting property of the matrix exponential is proven: For a real square matrix, where the log norm of the upper-left n by n block approaches negative infinity in a limiting process, the matrix exponential goes to zero in the first n rows and n columns. This property is useful for simplification of dynamic systems that exhibit modes with sufficiently different time scales; for example, in multi-loop...
This paper considers robust pole assignment problem for discrete-time linear periodic systems via linear periodic output feedback. To character a measure for the sensitivity of the eigenvalues of the closed-loop system with respect to perturbations in the coefficient matrices, a robustness index for periodic systems is proposed, which can be regarded as a generalization of robustness index of normal...
In this paper, it is researched the consensus problem via dynamic output feedback for linear time-invariant multi-agent systems (LTI-MASs) under fixed topologies. A linear matrix inequality approach for computing the feedback gain is obtained. A numerical simulation is given to illustrate the main result.
This paper is concerned with a set-point servo problem for MIMO systems with PldrSPRldrD control. The PldrSPRldrD control is constructed by introducing a SPR (strict positive real) element instead of the I element in PID control. The purpose is to design a PldrSPRldrD controller for asymptotic stabilization and to adjust P, SPR, D parameter matrices for improving convergence speed of responses under...
How to control an unstable linear system with a long pure delay in the actuator path? This question was resolved using dasiapredictorpsila or dasiafinite spectrum assignmentpsila designs in the 1970s. Here we address a more challenging question: How to control an unstable linear system with a wave PDE in the actuation path? Physically one can think of this problem as having to stabilize a system to...
In this paper a new methodology for decentralized overlapping tracking control of formations of autonomous unmanned vehicles based on the expansion/contraction paradigm is proposed. The methodology is based on a specific linear formation model. Decentralized controllers for the extracted subsystems are contracted to the original space after convenient modifications. It is proved that the overall closed...
This paper studies some properties of the recently developed parametric Lyapunov equation based low gain feedback design method. As applications of these new properties, alternative and simpler solutions are proposed to the (global) stabilization problem for a class of linear systems with input delay and the semi-global stabilization problem when the systems are in addition subject to actuator saturation...
This paper deals with the controllability of discrete-time linear systems with a time-invariant delay in state. As an improvement to existing definitions, a new controllability definition, which implies stabilizability and the existence of feedback controller for eigenvalue assignment, is introduced first. Then a necessary and sufficient criterion is developed to check the controllability. With this...
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