# A bounded real lemma for jump systems

@article{Seiler2003ABR, title={A bounded real lemma for jump systems}, author={Peter J. Seiler and Raja Sengupta}, journal={IEEE Trans. Autom. Control.}, year={2003}, volume={48}, pages={1651-1654} }

This note presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLSs). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for MJLSs.

## 151 Citations

A Bounded Real Lemma for Discrete‐Time Markovian Jump Singular Systems

- Mathematics, Engineering
- 2014

This paper presents a bounded real lemma for discrete‐time Markovian jump singular systems. First, a new necessary and sufficient condition is proposed in terms of a strict linear matrix inequality,…

Bounded Real Lemma for Nonhomogeneous Markovian Jump Linear Systems

- MathematicsIEEE Transactions on Automatic Control
- 2013

A bounded real lemma is established for discrete-time Markov jump linear systems with nonhomogeneous finite state Markov chain with different cases of arbitrary variation and periodic variation.

A Bounded Real Lemma for Discrete-time Systems with Stochastic Dynamics

- MathematicsTransactions of the Society of Instrument and Control Engineers
- 2019

The bounded real lemma for deterministic linear time-invariant systems is known as one of the most important tools in robust stability analysis. A counterpart for systems with stochastic dynamics is…

A strictly bounded real lemma for singular Markovian jump systems

- Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

The proposed BRL covers SMJSs with disturbance-contaminated output by introducing additional free matrix variables and represents LMI conditions which equal to strictly bounded realness, which can be used to obtaining the optimal optimal ℋ∞ performance.

On necessary and sufficient conditions for H∞ output feedback control of Markov jump linear systems

- MathematicsProceedings of the 45th IEEE Conference on Decision and Control
- 2006

It is shown that the feasibility of a set of linear matrix inequalities is both sufficient and necessary for the existence of a solution to the output feedback H∞ control problem for continuous-time Markov jump linear systems.

Bounded realness for discrete-time jump descriptor systems

- Mathematics2020 59th IEEE Conference on Decision and Control (CDC)
- 2020

To hold the necessity and sufficiency in terms of linear matrix inequality, two slack variables are introduced by coupling the variables and matrix in the null-space of the singular matrix in DJDSs.

A new approach for the H∞ control of Markov jump linear systems with partial information

- Mathematics, Computer Science2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

New results on H∞ analysis and control of linear systems with Markov jump disturbances, in a scenario of partial observations of the jump process, comprising a new Bounded Real Lemma and a condition for state feedback synthesis are presented.

Stability and disturbance attenuation for a switched Markov jump linear system

- MathematicsArXiv
- 2014

We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and…

## References

SHOWING 1-10 OF 30 REFERENCES

Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters

- Mathematics
- 1993

Stability results for discrete-time linear systems subject to random jumps in the parameters are obtained. First, necessary and sufficient conditions for mean square stability (MSS), including the…

Mixed / -Control of Discrete-Time Markovian Jump Linear Systems

- Mathematics
- 1998

In this paper we consider the mixed / -control problem for the class of discrete-time linear systems with parameters subject to Markovian jump linear systems (MJLS's). It is assumed that both the…

Stochastic stabilizability and H∞ control for discrete-time jump linear systems with time delay ☆

- Mathematics
- 1999

Discrete-time Markovian-jump linear quadratic optimal control

- Mathematics
- 1986

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic…

MIXED H 2 / H ~ CONTROL OF DISCRETE-TIME MARKOVIAN JUMP LINEAR SYSTEMS *

- Mathematics
- 1996

In this paper we consider the mixed Hz/H~-control problem for the class of discrete-time linear systems with parameters subject to Markovian jumps (MJLS). It is assumed that both the state variable…

Controllability, observability and discrete-time markovian jump linear quadratic control

- Mathematics
- 1988

This paper is concerned with the controllability and observability of discrete-time linear systems that possess randomly jumping parameters described by finite-stale Markov processes, and the…

H∞-Control of Markovian Jump Systems and Solutions to Associated Piecewise-Deterministic Differential Games

- Mathematics
- 1995

A class of linear-quadratic piecewise deterministic soft-constrained zero-sum differential games is formulated and solved, where the minimizing player has access to perfect or imperfect (continuous)…

Control with random communication delays via a discrete-time jump system approach

- Mathematics, Computer ScienceProceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)
- 2000

This work presents a V-K iteration algorithm to design switching and non-switching controllers for digital control systems with random but bounded delays in the feedback loop, with the transition jumps being modeled as finite-state Markov chains.

Stability of Linear Feedback Systems with Random Communication Delays

- Mathematics, Computer Science1991 American Control Conference
- 1991

In this report, necessary and sufficient conditions are found for zero-state mean-square exponential stability of the considered class of control systems.

Mixed H2/H∞-control of discrete-time Markovian jump linear systems

- MathematicsIEEE Trans. Autom. Control.
- 1998

This paper considers the mixed H/sub 2//H/sub /spl infin//-control problem for the class of discrete-time linear systems with parameters subject to Markovian jump linear systems, and presents an approximate version of these problems via linear matrix inequality optimization.