Unified dwell time–based stability and stabilization criteria for switched linear stochastic systems and their application to intermittent control

Abstract

Summary This paper considers the stability and stabilization problems for the switched linear stochastic systems under dwell time constraints, where the considered systems can be composed of an arbitrary combination of stable and unstable subsystems. First, a time‐varying discretized Lyapunov function is constructed based on the projection of a linear Lagrange interpolant and a switching‐time‐dependent “weighted” function. The “weighted” function not only enforces the Lyapunov function to decrease at switching instants but also coordinates the dynamical behavior of the subsystems. As a result, some unified criteria for mean square stability and almost sure stability of the switched stochastic systems are established in terms of linear matrix inequalities. Based on the obtained stochastic stability criteria, 2 types of state feedback controllers for the systems are designed. Moreover, the novel results are applied to solve the intermittent control or the controller failure problems. Finally, conservatism analysis and numerical examples are provided to illustrate the effectiveness of the established theoretical results.

Event‐triggered state‐dependent switching rule design for switched linear systems

“…where ′ = 2 1 , Q * 2 = ′ Q 2 , 1 , and 2 are arbitrary parameters. We could find the same feasible solution of P 1 , P 2 , Q 1 , and Q ′ 2 for both conditions (19) and (20) by setting variables of (20) as…”

“…There exist both time‐domain restrictions (for example, dwell time, average dwell time, mode‐dependent dwell time, mode‐dependent persistent dwell time) and state‐space restrictions for switching signals. Time‐domain restrictions mainly characterize time‐controlled switching laws and do not have constructive propositions.…”

“…[4][5][6][7][8] Daafouz et al 9 proposed a switched Lyapunov function approach for a discrete-time case to significantly reduce the conservativeness in stability analysis under arbitrary switching law. A new stability criterion with less conservativeness over a switched Lyapunov function approach was introduced in the work of Xiang et al 10 There exist both time-domain restrictions (for example, dwell time, [11][12][13][14] average dwell time, [15][16][17][18][19] mode-dependent dwell time, 20 mode-dependent persistent dwell time 21 ) and state-space restrictions for switching signals. Time-domain restrictions mainly characterize time-controlled switching laws and do not have constructive propositions.…”

Almost sure stability of second‐order nonlinear stochastic system with Lévy noise via sliding mode control

“…Stochastic system is a hot area in recent years. The usual sense stochastic noise is only driven by continuous Brown motion, which can describe continuous stochastic volatility. However, in many physical systems, there exist many types of discontinuous noise, such as random failures, abrupt change, and sudden disturbances.…”

Stabilization of stochastic Markovian switching systems on networks with multilinks based on aperiodically intermittent control: A new differential inequality technique

“…At present, various control strategies have been adopted to realize stability of SMSS, such as pinning control, feedback control, and intermittent control . Intermittent control is a kind of typical discontinuous feedback control strategy requiring control inputs to be activated during some work intervals, which reduces control cost and the amount of transmitted information than continuous feedback control .…”