H_∞ control for a class of discrete-time switched systems with state constraints

Abstract

This article investigates the H∞ control problem for a class of discrete-time switched systems with state constraints. The state constraints are converted into state saturations by limiting the state in a unit hypercube. An improved average dwell time method is presented to take into account different decay rates of a Lyapunov function related to an active subsystem according to whether the saturations occur or not. Switched state feedback controllers are designed such that the closed-loop switched system subjects to state constraints is asymptotically stable and achieves a weighted L2-gain. Sufficient conditions for H∞ control of the switched system with state constraints are first derived. An application to a longitudinal motion of highly maneuverable aircraft technology vehicle is given to illustrate the applicability and the effectiveness of the proposed method.

Stabilization of a Class of Continuous-Time Switched Systems with State Constraints via a Mode-Dependent Switching Method

“…therefore, the continuous-time switched system with state constraints (23) is GUAS with MDADT satisfying (18).…”

“…Many techniques have been studied in the study of switched systems, for example, common Lyapunov function, multiple Lyapunov functions, and switched Lyapunov functions [15][16][17]. However, the average dwell time method is generally recognized to have more flexibility in stabilization for switched systems [18][19][20][21][22][23].…”

Stabilization of a class of switched systems with state constraints via time-varying Lyapunov functions

“…In the study of switched systems with partial state constraints, different approaches, for example, barrier Lyapunov function method and nonlinear model predictive control, have been proposed over the last few years. For the switched systems defined on a closed hypercube as all state variables are constrained to the unit hypercube, different problems have been investigated in, for example, Su and Zhao (2012, 2014), Su and Wang (2015), Su et al (2018), Zhao and Zhao (2020), and Wu et al (2021). Based on the “min-switching” strategy, Zhao and Zhao (2020) investigated the issue of H ∞ reliable bumpless transfer control problem.…”

“…However, to the best of the authors knowledge, the results of how to eliminate the effects of “jump” phenomena by proposing different time-varying Lyapunov functions for switched systems with state constraints by limiting the state in a unit hypercube have not been reported in the literature. In addition, the total times ( R p ( 0 , t ) and S p ( 0 , t ) ) of each subsystem during which the state is saturated or non-saturated within [ 0 , t ) separately should be calculated in Su and Zhao (2012, 2014), Su and Wang (2015), and Su et al (2018). However, there is no calculation method for these parameters in Su and Zhao (2012, 2014), Su and Wang (2015), and Su et al (2018), which makes it difficult to calculate these parameters, and thus difficult to guide switching signal design.…”

Stabilization of state‐constrained switched nonlinear systems in p‐normal form

“…In recent years, the study of switched systems has received considerable attention. Focus has been put on stability analysis and feedback stabilization and many other issues . Meanwhile, because of explicit engineering background and extensive application prospects, switching control is progressively applied to networks , fault detection and isolation , aeronautics and astronautics , and so on.…”