Abstract
This paper proposes an ℋ 2 state-feedback controller for Markovian jump systems with input saturation and incomplete knowledge of transition probabilities. The proposed controller is developed using second-order matrix polynomials of an incomplete transition rate to derive less conservative stabilization conditions. The proposed controller not only guarantees ℋ 2 performance but also rejects matched disturbances. The effectiveness of the proposed method is demonstrated using three numerical examples.
Highlights
Over the last few decades, Markovian jump systems (MJSs) have been recognized as one of the most effective models for the representation of dynamic systems subjected to random and abrupt variations. us, numerous studies have been conducted to analyze and synthesize MJSs [1,2,3,4,5,6,7]. e findings of these studies have been applied in various practical systems, such as networked control systems [8], manufacturing systems [8], economic systems [9], power systems [10], and actuator saturation [11]
Such MJSs with exactly known transition probabilities have limited scope for application in practical systems because it is difficult to obtain complete knowledge of transition probabilities. us, recent studies on controller synthesis have focused on MJSs with incomplete knowledge of transition probabilities
Based on the proposed relaxation method using the second-order matrix polynomials of the incomplete transition rate, this paper presents less conservative stabilization conditions for estimating the domain of attraction
Summary
Over the last few decades, Markovian jump systems (MJSs) have been recognized as one of the most effective models for the representation of dynamic systems subjected to random and abrupt variations. us, numerous studies have been conducted to analyze and synthesize MJSs [1,2,3,4,5,6,7]. e findings of these studies have been applied in various practical systems, such as networked control systems [8], manufacturing systems [8], economic systems [9], power systems [10], and actuator saturation [11]. Us, recent studies on controller synthesis have focused on MJSs with incomplete knowledge of transition probabilities. The stochastic stabilization problem for MJSs subjected to actuator saturation was studied based on exactly known transition probabilities [21, 22]. The stabilization of saturated MJSs with incomplete knowledge of transition probabilities was studied using the free-connection weighting matrix approach [11]. Us, an H2 stabilization condition for MJSs with input saturation and incomplete knowledge of transition probabilities is proposed . E main contributions of this study are as follows: Mathematical Problems in Engineering is is the first proposal to propose a stabilization condition to accomplish stochastic stability and guarantee H2 performance for MJSs with input saturation and incomplete knowledge of transition probabilities. We use ‖x‖p to indicate the p-norm of x, i.e., ‖x‖p ≜ (|x1|p + · · · + |xn|p)(1/p), p ≥ 1. λmin(X) and λmax(X) denote a minimum eigenvalue and a maximum eigenvalue of X, respectively. e notation ek indicates a unit vector with a single nonzero entry at the kth position, i.e., ek ≜ [0 . . . 1 . . . 0]T
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