Control For Discrete-time Singular Systems Research Articles

New LMI approach to [formula omitted] control of discrete-time singular systems

This article studies the problem of feedback H∞ control for discrete-time singular system. The objective is to design the controller to make the closed-loop system admissible and satisfy the specified H∞ performance. Firstly, the admissibility of the closed-loop system is analyzed via the Lyapunov function and linear matrix inequality (LMI) method, the admissibility condition of the singular system with H∞ performance is given. Then, applying a useful matrix inequality lemma, the controller design condition for discrete-time singular system is shown by a LMI. Specially, the benefit of the proposed design result is their less conservatism, the validity of the viewpoint is proposed by numeric illustrations.

Admissibility Analysis and Control for Discrete-Time Singular Systems with Interval Time-Varying Delay

This paper mainly investigates an admissibility analysis and controller design problem for an uncertain discrete-time singular system with delayed states. The time-varying delay is within an interval whose lower bound may be greater than zero. Using a modified finite sum inequality and choosing a suitable Lyapunov-Krasovskii function, we derive a set of LMI-based sufficient delay-dependent conditions for the admissibility analysis and controller synthesis problem, respectively. In the end, a numerical example shows the effectiveness and validity of the proposed approach.

Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems

In this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimizing the addition of the quadratic norm of the tracking-error vector and the weighed quadratic norm of the compensation vector. By virtue of the elementary permutation matrix and the property of the quadratic function, the optimized-gain vector is solved and explicitly expressed by the system Markov matrix and the iteration-wise tracking error. Then the linearly monotonic convergence of the tracking error is derived under the assumption that the initial state of the dynamic subsystem is resettable. Furthermore, for the circumstance that the system parameters uncertainties exist, the quasi scheme is established by replacing the exact system Markov matrix with the approximated one in the optimized gain. Rigorous analysis conveys that the proposed gain-optimized scheme is robust to the system internal disturbance within a suitable range. The validity and effectiveness are demonstrated numerically.

Convergence characteristics of iterative learning control for discrete-time singular systems

This paper investigates the convergence characteristics of the conventional P-type iterative learning control (ILC) scheme and exploits a gain-adaptive iterative learning control mechanism for a class of linear discrete-time singular systems. Based on the lifted vector technique, the paper reforms the discrete-time singular system as a kind of algebraic input-output transmission. For the conventional P-type ILC scheme, the asymptotical convergence in terms of the tracking-error vector is achieved and the monotonic convergence in the sense of 2-norm of the tracking-error vector is derived. Further, in order to improve the learning performance, a gain-adaptive iterative learning control (GAILC) strategy is developed, which argues the iteration-time-variable gain vector while minimising the increment of quadratic tracking-error vectors of two adjacent iterations. The existence of the optimal gain vector is explored through the optimisation criterion and the algebraic approach of the columns/ rows exchanging transformation of matrix. Then the non-conditionally strictly monotonic convergence of the GAILC is made by studying the eigenvalues of the quadratic function. Finally, the validity and the effectiveness of the P-type ILC are numerically demonstrated and the remarkable outcomes of the GAILC are illustrated.