Robust partial sampled-data state feedback control of Markov jump linear systems

Abstract

This paper proposes new conditions for the design of a robust partial sampled-data state feedback control law for Markov jump linear systems (MJLS). Although, as usual, the control structure depends on the Markov mode, only the state variable is sampled in order to cope with a specific network control structure. For analysis, an equivalent hybrid system is proposed and a two-point boundary value problem (TPBVP) that ensures minimum H ∞ or H 2 cost is defined. For control synthesis, it is rewritten as a convex set of sufficient conditions leading to minimum guaranteed cost of the mentioned performance classes. The optimality conditions are expressed through differential linear matrix inequalities (DLMIs), a useful mathematical device that can be handled by means of any available LMI solver. Examples are included for illustration.

Robust consensus tracking of one‐sided Lipschitz nonlinear multi‐agent systems under structured uncertainty and time‐varying delay

“…Pre-and post-multiplying ( 17)-( 19) by Θ T 1 and Θ 1 , respectively, we have ( 34)- (36). Pre-and post-multiplying ( 16) by Θ T 2 and Θ 2 , (33) is obtained.…”

“…However, in reality, only partial system states may be measurable, and some distinct partial-state feedback controllers have been developed. [34][35][36] After considering the previous discussions, it is evident that although some remarkable results have been obtained, the consensus tracking of MASs with OSL nonlinear dynamics, structured uncertainty, and time-varying communication delay has not been widely studied. The primary contributions of this article are as follows: (1) This article considers all three factors together in MASs, which makes the problem more challenging than studying them separately as done in existing studies.…”

Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics

“…Problem Statement. Several MJLS control problems have been studied, such as stability [12,56], H ∞ -controller design [19,21,22,55], and optimal control [30,54]. However, limited research has been done for more complex tasks expressed in, for example, PCTL.…”

Event-triggered Observer-based Robust H∞ Fault-tolerant Control for Markov Jumping NCSs

“…At the same time, network states are random, while the Markov process is also a random process, so this latter can accurately show the states of network systems. Based on the above characteristics, the research of NCSs can be regarded as the research of systems with Markov process [16][17][18][19][20]. Specifically, the Markov jumping system is a random hybrid system with Markov process.…”