HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 28 May 2022 20:29:10 GMT2022-05-28T20:29:10Z5051- On Smith-type iterative algorithms for the Stein matrix equationhttp://hdl.handle.net/10722/124889Title: On Smith-type iterative algorithms for the Stein matrix equation
Authors: Zhou, B; Lam, J; Duan, GR
Abstract: This note studies the iterative solution to the Stein matrix equation. Firstly, it is shown that the recently developed Smith(l) iteration converges to the exact solution for arbitrary initial condition whereas a special initial condition is required in the literature. Secondly, by presenting a new accelerative Smith iteration named the r-Smith iteration that includes the well-known ordinary Smith accelerative iteration as a special case, we have shown that the r-Smith accelerative iteration requires less computation than the Smith iteration and the Smith(l) iteration, and the ordinary Smith accelerative iteration requires the least computations comparing with other Smith-type iterations. © 2009 Elsevier Ltd. All rights reserved.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1248892009-01-01T00:00:00Z
- Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approachhttp://hdl.handle.net/10722/157059Title: Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach
Authors: Shu, Z; Lam, J; Xiong, J
Abstract: This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical examples. © 2010 Elsevier Ltd. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1570592010-01-01T00:00:00Z
- Robust H2 control of Markovian jump systems with uncertain switching probabilitieshttp://hdl.handle.net/10722/59035Title: Robust H2 control of Markovian jump systems with uncertain switching probabilities
Authors: Xiong, J; Lam, J
Abstract: This article deals with the robust H2 control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H2 performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H2 performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/590352009-01-01T00:00:00Z
- Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuatorshttp://hdl.handle.net/10722/157025Title: Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuators
Authors: Haidar, A; Boukas, EK; Xu, S; Lam, J
Abstract: This study deals with the class of continuous-time singular linear systems with time-varying delays. The stability and stabilisation problems of this class of systems are addressed. Delay-range-dependent sufficient conditions such that the system is regular, impulse free and α-stable are developed in the linear matrix inequality (LMI) setting and an estimate of the convergence rate of such stable systems is also presented. An iterative LMI (ILMI) algorithm to compute a static output feedback controller gains is proposed. Some numerical examples are employed to show the usefulness of the proposed results. © 2009 The Institution of Engineering and Technology.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1570252009-01-01T00:00:00Z
- Weighted H ∞ filtering of switched systems with time-varying delay: Average dwell time approachhttp://hdl.handle.net/10722/157040Title: Weighted H ∞ filtering of switched systems with time-varying delay: Average dwell time approach
Authors: Wu, L; Lam, J
Abstract: This paper is concerned with the H ∞ filtering problem for a continuous-time linear switched system with time-varying delay in its state. To reduce the overdesign of the quadratic framework, this paper proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. By using an average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability with a weighted H ∞ performance for the filtering error system with the decay estimate explicitly given. Then, the corresponding solvability condition for a desired filter is established, and the filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. All the conditions obtained in this paper are delay dependent. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory. © 2009 Birkhäuser Boston.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1570402009-01-01T00:00:00Z