Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme

Highlights：

• To formulate the observer-based stabilization conditions in terms of LMIs, two additional goals must also be reachable. The first goal is to embrace a one-step design strategy that simultaneously designs both fuzzy observer and control gains without any iteration procedures, which is achieved by constructing a nonquadratic Lyapunov function with real and estimated states and by employing a positive tuning parameter. The second goal is to effectively relax the time-varying transition probabilities included in the stabilization conditions, which is achieved via a modified relaxation technique that can avoid excessive use of slack variables.

• As mentioned above, this paper presents the first attempt in the discretetime domain to design an observer-based output-feedback control of nonhomogeneous MJFSs with uncertainties. Furthermore, by turning some time-varying parameters into constants, the main stabilization conditions of this paper can also be utilized in the control design of fundamental systems such as uncertain T-S fuzzy systems, uncertain Markovian jump linear systems, and homogeneous MJFSs.

摘要

•Based on the mode-dependent nonquadratic Lyapunov function, this paper proposes a novel method to design an observer-based non-PDC controller by means of congruent transformation. Specifically, the non- PDC control scheme requires the use of a congruent transformation with two fuzzy-basis-dependent variables, which forces the stabilization conditions to be dependent on the nonconvex terms in which the two variables are combined. To solve such a nonconvex problem, this paper presents a decoupling technique that extracts the nonconvex terms from the stabilization conditions, where the used slack variables are set to be fuzzy-basis-dependent for less conservative performance.•To formulate the observer-based stabilization conditions in terms of LMIs, two additional goals must also be reachable. The first goal is to embrace a one-step design strategy that simultaneously designs both fuzzy observer and control gains without any iteration procedures, which is achieved by constructing a nonquadratic Lyapunov function with real and estimated states and by employing a positive tuning parameter. The second goal is to effectively relax the time-varying transition probabilities included in the stabilization conditions, which is achieved via a modified relaxation technique that can avoid excessive use of slack variables.•As mentioned above, this paper presents the first attempt in the discretetime domain to design an observer-based output-feedback control of nonhomogeneous MJFSs with uncertainties. Furthermore, by turning some time-varying parameters into constants, the main stabilization conditions of this paper can also be utilized in the control design of fundamental systems such as uncertain T-S fuzzy systems, uncertain Markovian jump linear systems, and homogeneous MJFSs.