Finite‐Time H₂/H_∞ Control for Linear Itô Stochastic Systems with (x, u, v)‐Dependent Noise

Abstract

This paper deals with the problem of the H2/H∞ control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the H2/H∞ control does not involve systems’ transient performance. To express this problem clearly, a concept called finite-time H2/H∞ control is introduced. Moreover, state feedback and observer-based finite-time H2/H∞ controllers are designed, which guarantee finite-time boundedness, H2 performance index, and H∞ performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time H2/H∞ control is presented to obtain the minimum values of the H2 index and H∞ index. Finally, we use an example to show the validity of the obtained results.

Finite-Time H2/H∞ Control Design for Stochastic Poisson Systems with Applications to Clothing Hanging Device

“…Nowadays, the problems of FTS and FTB have been deeply investigated (see, e.g., [26][27][28][29][30][31][32][33][34][35][36]). In consideration of the merits of FTB and H 2 /H ∞ control, the finite-time H 2 /H ∞ control for stochastic systems with Wiener noise is first presented in [37], which satisfies both FTB and H 2 /H ∞ performance index. However, in many practical systems, it is not only disturbed by Wiener noise, but also by Poisson noise.…”

“…(i) Unlike the model considered in [37], this paper studies the model of stochastic Poisson systems with Wiener and Poisson noises. e former considers only Wiener noise, and the latter considers both Wiener and Poisson noises.…”

“…Moreover, in the former model, the measurement output y(t) is composed of only the state, but the measurement output considered in the latter model is composed of both the state and external interference. e latter model is more general than the former model in [37], which is used to model many real systems.…”

“…(ii) e two theorems ( eorems 2 and 4) are obtained to guarantee the existence of state feedback finitetime (SFFT) and observer-based finite-time (OBFT) H 2 /H ∞ controllers, respectively. e two theorems ( eorems 2 and 4) contain the parameters both α and Poisson jump intensity λ, which are complex than the corresponding conditions in [37]. By adjusting the two parameters, the most satisfying finite-time H 2 /H ∞ controllers will be designed.…”

“…By adjusting the two parameters, the most satisfying finite-time H 2 /H ∞ controllers will be designed. (iii) A new optimization algorithm constrained by matrix inequality is proposed to demonstrate the relationships among α, λ, and optimal H 2 /H ∞ index, which is more complex than that in [37].…”