Generalized H 2 control of the linear system with semi‐Markov jumps

In this work we study the design of filters for phase‐type (PH) semi‐Markov jump linear systems, considering partial information on the system's operating mode and possible parameter uncertainties. With respect to the mode of operation, it is assumed that the state space of the semi‐Markov chain can be written as the union of disjoint sets, called clusters, and the only information available to the filter is which cluster the state of the semi‐Markov chain belongs to. A new linear matrix inequality (LMI) parameterization employing the slack variable technique is introduced for the design of switching full‐order filters according to the cluster observations so that suitable bounds on the norm of the estimation error are guaranteed for the uncertain system. If the system is restricted to be a Markov jump linear system and the Markov chain is assumed to be perfectly measured, the design conditions are shown to be also necessary leading to the optimal full‐order filter. Furthermore, the general filter can be particularized into an observer form for the case in which the system matrices are the same within each cluster and there are no parameter uncertainties except for possible uncertainties affecting the transition rates of the jumping process. The paper concludes with an illustrative example in the context of networked control systems.

“…Definition 2 (Mean-square stability (MSS), Costa et al 3 ). Set w = 0 in (11). System ( 11) is said to be MSS if lim t→∞ E(||x(t)|| 2 ) = 0 for arbitrary x 0 ∈ R 2n x and Z(0…”

Section: Problem Formulationmentioning

confidence: 99%

Robust H₂ filtering of phase‐type semi‐Markov jump linear systems with cluster observations

de Oliveira,

Costa

2024

“…When it comes to the controller design for SMJSs, most existing results are built on the basis of the assumption that the plant mode is fully available to the controller. [6][7][8][9][10][11][12][13] Then the mode switching of controller can be synchronous with the plant. This assumption, however, is not realistic in practical applications.…”

Section: Asynchronous Controllermentioning

confidence: 99%

“…First, we will derive conditions on FTSB for the augmented closed-loop system (9) and then present an approach to solve the FTSD analysis.…”

Section: Ftsd Performance Analysismentioning

confidence: 99%

“…This consequently results in the transition rates in SMJSs being time‐varying and dependent on the sojourn time, which also brings the main difficulties in analysis and synthesis of SMJSs. Up to now, an increasing attention have been paid to SMJSs and many interesting results have emerged, see for instance, stability and stabilization, 6‐8

{H}_2

control, 9

{H}_{\infty }

control, 10 finite‐time control, 11 event‐triggered control, 12 sliding mode control, 13 energy‐to‐peak filtering, 14 distributed filtering, 15 and on forth.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite‐time stochastic dissipative output tracking control of semi‐Markov jump systems via an adaptive event‐triggered mechanism

Shi

2023

This work focuses on the output tracking control for a class of continuous-time semi-Markov jump systems (SMJSs). In the controller design, not only the finite-time stochastic boundedness (FTSB), but also the dissipative performance over a finite-time interval is considered. In order to save communication resources, a version of adaptive event-triggered mechanism (AETM) is utilized. Different from the traditional static event-triggered mechanism, the threshold coefficient in AETM is time-varying and can be adjusted in real-time to fit the system evolution. Moreover, the asynchronous switching between the controller modes and the plant modes is taken into account. The design objective is to synthesis an adaptive event-triggered asynchronous state-feedback controller such that not only the augmented closed-loop system is FTSB with a certain level of dissipative performance, but also the communication burden can be reduced to some extent. It is the first attempt to investigate the output tracking control of SMJSs over a finite-time interval. By constructing a plant model-dependent Lyapunov function, a set of conditions is derived for the FTSB analysis, based on which a controller design algorithm is presented. Finally, an illustrative example is given to verify the availability of the theoretical findings.

“…In recent years, much attention has focused on the stability analysis and stabilization synthesis of Markov jump systems (MJSs; see References 1‐6) and semi‐Markov jump systems (SMJSs; see References 7‐18). The important advance of these works is the generalization of their stochastic switching signal from a Markov process (MP) to a semi‐Markov process (SMP).…”

Section: Introductionmentioning

confidence: 99%

The observed mode dependent controller design problem for a class of continuous‐time hidden semi‐Markov jump systems

Wang

Zhu

2023

SummaryThis paper studies the stability analysis and stabilization synthesis problems for a class of continuous‐time jump systems with hidden system modes. To precisely model the switching signals of the considered systems, a novel definition of continuous‐time hidden semi‐Markov process is proposed based on the notions of emission probability and time varying dual‐index transition rate. By virtue of such definition, a dual‐index Lyapunov function is utilized to derive the sufficient stability conditions of the considered systems. By adopting a technology that can decouple the nonlinear terms in the above conditions, the numerically testable existence conditions of the controller for the resulting stabilizing systems are presented. An example is given to illustrate the effectiveness of our results.