Quadratic stabilizability and H_∞ control of linear discrete‐time stochastic uncertain systems

Abstract

This paper considers quadratic stabilizability and H∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l2‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H∞ state and output feedback H∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H∞ controllable. Sufficient conditions for the existence of the desired robust H∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.

H∞ Optimal Performance Design of an Unstable Plant under Bode Integral Constraint

“…There is another type of unstable plants such as a magnetic levitation system, which has been built in some universities at home and abroad. But these systems could not run, and there exists a large peak in the data of sensitivity function [4]. And after X-29, the unstable poles are considered under the research on the Fight Aircraft JAS-39 and X-30, which succeeds.…”

“…For example, γ = 1 means 1 N responds 1 m with Figure 7: Model of the electromagnetic levitation system. 4 Complexity disturbance force and displacement in (12), which requires the index of the system smaller than 1 m/N = 10 3 mm/N. This is available for the system with mm dimension, which is an index with γ = ∞ and is of no use.…”

H∞ Tracking Control for Nonlinear Fractional-Order Systems Via Output Feedback Design

“…(24) Using inequalities (23), (24) and the fractional direct Lyapunov method in Lemma 1, the sufficient condition can be written as…”

“…Performances were also considered in [10], where a method to evaluate the H2 norm of a FO system. Furthermore, concerning the extension of H∞ theory [24] to FO systems, analysis results on the computation of H∞ norm for FO system have recently been published in [6]. The H∞ state feedback and output feedback controllers for FO systems were proposed in [7] and [13], respectively.…”

Direct Adaptive Fuzzy Backstepping Control for Stochastic Nonlinear SISO Systems with Unmodeled Dynamics

“…However, [1][2][3][4][5][6][7][8] ignore the stochastic disturbance. It is generally known that stochastic disturbance is a troublesome source which could lead to the instability of control systems, and it exists in most practical systems [9][10][11][12][13][14], especially in aerospace systems, industrial control of power systems, dynamics of epidemic diseases [15,16], and linear quadratic optimal control [17][18][19][20]. Therefore, adaptive control for stochastic nonlinear systems has received considerable attention [21][22][23][24].…”