Generalized H₂ control of discrete‐time semi‐Markov jump systems

Abstract

This paper mainly studies the generalized H2 control of discrete‐time semi‐Markov jump systems with bounded sojourn‐time. By constructing the mode‐dependent Lyapunov function related to the elapsed‐time and the semi‐Markov process, we obtain sufficient conditions to ensure the σ‐error mean square stable and generalized H2 performance of the semi‐Markov jump system. Moreover, by introducing slack variables, the generalized H2 performance index is reduced and the feasible region is expanded. Finally, through numerical calculations, we confirm the effectiveness of the design methods.

Modified Riccati iterative algorithms for stochastic coupled algebraic Riccati equations of linear stochastic Markovian jump systems

“…Among these studied problems, the linear quadratic regulator (LQR) problem has attracted a lot of attention in the field of control theory and applied mathematics [13][14][15][16], and its main idea is to design a feedback control law(mostly linear) so that the given quadratic performance index can be optimized, and the LQR problem of linear stochastic systems with Markovian jumps is discussed, see [17][18][19][20][21].…”

Dual asynchronous control for T‐S fuzzy semi‐Markov jump systems: A finite‐time design

“…As a matter of fact, the sojourn time might follow any distribution, and the transition rates can be time-varying in a finite mode set. Under this context, the concept of semi-Markov jump systems (SMJSs) with sojourn time-dependent transition probabilities have been proposed with burgeoning research attention [27][28][29]. This improvement can release above strict modeling restrictions on MJSs and boost potential applications.…”