Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

Abstract

a b s t r a c tThis 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.

Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance

“…Markovian jumping systems (MJSs), involve both time-evolving and event-driven mechanisms, have received extensive research attention in the past few decades (Shu, Lam, & Xiong, 2010;Zhang, Wang, & Chen, 2009). Both the analysis and synthesis for MJSs have been extensively studied, see (Xiong, Lam, Shu, & Mao, 2014;Zhang, 2009) and the references therein.…”

H∞ Control for Markov Jump Systems with Nonlinear Noise Intensity Function and Uncertain Transition Rates

“…However, in the stability analysis of [16,17], the traditional Young inequality is used to bound the uncertain term s j=1π ij P j . Such bounding technique produces the quadratic form of P j − P i (for example, in [17] the quadratic terms [18]. Based on the bounding technique of [17], a LMI method for controller design is proposed in [26], but it is at the expense of the increase of conservatism (i.e., the method in [26] has a higher conservatism than that of [17]).…”

“…Due to the use of Young inequality, the proposed controller design methods in both [16] and [17] need to solve a set of nonlinear matrix inequalities (NLMIs). Unfortunately, such NLMIs cannot still be completely solved up to now [18]. Moreover, in the existing literatures, only linear MJSs with uncertain transition rates were studied.…”

Static output‐feedback controller design for vehicle suspensions: an effective two‐step computational approach

“…The design of this kind of controllers, however, leads to challenging theoretical problems and serious computational difficulties [11,16]. To provide a practical solution to these problems, a variety of multi-step numerical algorithms have been proposed, which allow finding suboptimal solutions with a reasonable computational cost [17][18][19][20][21][22][23][24][25]. These heuristic approaches typically involve a number of free parameters and, for a practical application of the method, a suitable set of parameter values has to be determined.…”