An improved delay-dependent stabilization criterion of linear time-varying delay systems: An iterative method

summary:This paper presents delay-dependent stabilization criteria for linear time-varying delay systems. A less conservative stabilization criterion is derived by invoking a new Lyapunov-Krasovskii functional and then, extended reciprocally convex inequality in combination with Wirtinger's inequality is exploited to obtain an improved stabilization criterion where a set of nonlinear matrix inequalities is solved by applying the cone complementarity algorithm. The proposed stabilization technique transforms a non-convex problem into a nonlinear trace minimization problem which is solved by an iterative approach. Numerical examples are considered to demonstrate the effectiveness of the proposed stabilization criteria and the presented iterative algorithm outperforms some existing results

Existence of pole-zero structures in a rational matrix equation arising in a decentralized stabilization of expanding systems

summary:A necessary and sufficient condition for the existence of pole and zero structures in a proper rational matrix equation $T_{2} X = T_{1}$ is developed. This condition provides a new interpretation of sufficient conditions which ensure decentralized stabilizability of an expanded system. A numerical example illustrate the theoretical results

Design of reaching phase for variable structure controller based on Householder transformation

summary:The paper presents control signals generation methods, preventing the excitation of residual vibration in slightly damped oscillational systems. It is focused on the feedforward methods, as most of the vibrations in examined processes are induced by the control, while the influence of disturbances is mostly negligible. Application of these methods involves ensuring of the insensitivity to natural frequency change, which can be reached in classical approach only by considerable increase of transient response duration. Genetic algorithms can be effectively applied for the numerical optimization of developed shaper while maintaining the insensitivity to parameter change and short time delay

Necessary and sufficient conditions for stabilization of expanding systems servomechanism problems

summary:The problem of designing realistic decentralized controller to solve a servomechanism problem in the framework of “large scale systems” is considered in this paper. As any large scale system is built by expanding construction of one subsystem being connected to the existing system. In particular, it is desired to find a local stabilizing controller in terms of a free parameter (belonging to the ring of proper stable transfer functions) so that desirable properties of the controlled system, such as tracking and/or disturbance rejection for any arbitrary deterministic signal along with stabilization of the expanded overall system occur. An algorithm for designing such a free controller parameter is presented. The necessary and sufficient conditions for the existence of solutions to the Expanding Systems with Tracking and/or Disturbance Rejection Problem are established here and characterized the corresponding full set of stabilizing controllers that solve the problem. A numerical example is presented to illustrate the design procedure of the proposed controller for the Expanded System