Dissipative State Feedback Research Articles

Finite-region dissipative control for 2-D switched systems via mode-dependent average dwell time

Dissipativity is a significant concern for 2-D switched systems, but existing research often overlooks the transient dynamics occurring within a finite region. This paper aims to address finite-region dissipativity and dissipative control for a class of Fornasini-Marchesini local state-space (FMLSS) type 2-D switched systems. The analysis employs the mode-dependent average dwell time approach. Firstly, the concept of dissipativity on finite-region for 2-D switched systems is introduced. Then, a sufficient condition under which the considered systems can demonstrate the finite-region boundedness with the external disturbances is established by the special recursive formulas. Additionally, a sufficient condition for finite-region dissipativity of the considered systems is provided. Furthermore, the dissipative state feedback controller is derived to ensure the finite-region dissipativity of the closed-loop systems. To illustrate the effectiveness of the proposed controller design approach, an example is presented.

Conservatism reduction in robust control of Markov jump delay systems

A new method is developed for the robust stabilization of a Markov jump system with general discrete state time-delay and partly unknown transition probabilities. In contrast to most existing literature, a set of numerical testable conditions, rather than a huge matrix inequality, are established for the resulting closed-loop system in order to justify the stochastic stability and disturbance attenuation capability with the aid of a non-monotonic design approach. To be specific, by constructing a stochastic Lyapunov function via the application of an n-samples variation, sufficient conditions for the existence of a dissipative state feedback controller are derived with less conservativeness, that is, with larger stochastic stable region and better attenuation level. Three examples including a numerical example, a pest’s structured population model and an F-404 test aircraft model are presented to demonstrate the advantage and practical potential of the proposed methodology.

Dissipative stabilization of linear systems with time-varying general distributed delays

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system’s states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovskiĭ functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.

Dissipative Control of 2-D Switched Discrete System Via Dwell-Time-Dependent Approach

This paper studies the dissipative control problem for two-dimensional (2-D) switched discrete-time linear system represented by Fornasini–Marchesini local state-space (FMLSS) model via dwell-time-dependent Lyapunov function (DTDLF) approach. Consider the definition of (Q, S, R)- $$\alpha $$ -dissipativity for 2-D switched discrete FMLSS model in triangular region and based on the DTDLF approach, we first give the linear matrix inequality (LMI)-based sufficient condition on asymptotic stability for the 2-D switched discrete FMLSS model and then propose the LMI-based sufficient condition which can guarantee the given 2-D switched system to be asymptotically stable and strictly (Q, S, R)- $$\alpha $$ -dissipative. Furthermore, the dwell-time-dependent dissipative state-feedback controller is designed, and the LMI-based sufficient condition for designing such controller is proposed. Besides, dwell-time-dependent passive state-feedback controller and dwell-time-dependent $$H_\infty $$ state-feedback controller could be derived as the special cases of dissipative control from the established result. Finally, illustrative examples are depicted to verify the efficiency and superiority of the proposed techniques.

Dissipative control for singular time-delay system with actuator saturation via state feedback and output feedback

ABSTRACTThis paper is devoted to the problem of dissipative control for a class of singular time-delay systems with actuator saturation via state feedback and output feedback. First, by tuning the Wirtinger-based integral and the double integral inequality, a sufficient condition is derived to guarantee that the singular time-delay system is regular, impulse free, asymptotically stable and strictly (Q,S,R)-dissipative. Then, based on the derived condition, and applying linear matrix inequality techniques, the dissipative state feedback and output feedback controller are synthesised. Moreover, the maximal estimate of the domain of attraction is proposed by an optimisation problem. Finally, some simulation examples are provided to verify the effectiveness of the obtained theoretic results.

이산시간 불확실 특이시스템의 유한시간 강인 산일성 상태궤환 제어기 설계

In this paper, we treat the problem of a robust finite-time dissipative state feedback controller design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for finite-time stability of discrete-time singular systems is derived. A finite-time dissipative state feedback controller design method satisfying finite-time stability and dissipativity is proposed by LMI(linear matrix inequality) technique on the basis of the obtained BRL. Moreover it is shown that the obtained condition can be extended into polytopic uncertain systems by proper manipulations. Finally, illustrative examples are given to show the applicability of the proposed method.

Two-Dimensional Dissipative Control and Filtering for Roesser Model

This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative. Special cases, such as 2-D passivity performance and 2-D $H_{\infty} $ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties . This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests . The developed results in this paper for the nominal system encompass available results on H ∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.

Robust Impulse Dissipative Control of Singular Systems with Uncertainties

Based on the linear matrix inequality (LMI) method, this paper discusses the impulse dissipative problem for a class of singular systems with uncertainties under the description of state-space, and obtains the robust impulse dissipative state feedback controller and output feedback controller for singular systems with allowable uncertainties by solving the linear matrix inequalities. At last, we testify the feasibility of our results by a numerical example.