Singular Hybrid Systems Research Articles

Static output feedback quantized dissipative security control of singular hybrid systems subject to multiple cyber attacks: A dynamic-memory event-triggered strategy

This paper researches the problem of dynamic-memory event-triggered quantized dissipative security control for singular Markovian jump systems (SMJSs) subject to multiple cyber attacks, which comprise denial of service (DoS) attacks and multichannel deception attacks. By employing a set of historically released packets, a dynamic-memory event-triggered strategy is developed subject to DoS attacks which can decrease the occupancy rate of network communication bandwidth and achieve desired dissipative control performance. Furthermore, the closed-loop SMJSs are established by a switched system model on account of the simultaneous appearance of DoS attacks and deception attacks By constructing an improved mode-dependent piecewise Lyapunov–Krasovskii functional and applying singular value decomposition technique, the criteria of exponential admissibility and strict dissipativity for the controlled SMJSs are acquired by right of linear matrix inequalities. The idiographic form of the static output feedback quantized controller is expressed via a valid decoupling method. Finally, the validity of the proposed approach is testified by a numerical example and direct current motor driven load.

Robust $$H_\infty $$ asynchronous fault detection for uncertain singular hybrid systems based on Hmm strategy

Robust $$H_\infty $$ asynchronous fault detection for uncertain singular hybrid systems based on Hmm strategy

Output feedback [formula omitted] control for singular hybrid systems with partly unknown transition rates and input saturation

This paper investigates dynamic output feedback H∞ control for singular Markovian jump systems with partly unknown transition rates and input saturation. Necessary and sufficient conditions that singular Markovian jump system satisfies stochastic admissibility and H∞ performance index are successfully deduced in terms of linear matrix inequalities under the two different conditions of completely known transition rates and partly unknown transition rates. Mode-dependent dynamic output feedback controller is designed to ensure that the closed-loop singular Markovian jump system satisfies stochastic admissibility and H∞ performance index. Novel set invariant condition is proposed, and it not only provides an estimate of the attractive domain of the closed-loop system but also allows the analysis of performance outside the stability region within this invariant set. Furthermore, the estimation of the attraction domain comes down to the determination of the largest contractively invariant ellipsoid satisfying the necessary and sufficient conditions and the novel set invariant condition, and it is solved as an optimization problem with linear matrix inequality constraints. Finally, the effectiveness and utility of the proposed method are verified by a numerical example and an oil catalytic cracking process.

A positive real lemma for singular hybrid systems

Abstract This paper introduces a positive real lemma for continuous-time singular hybrid systems. The necessary and sufficient condition of stochastic admissibility and strict passivity for the singular hybrid systems is obtained in terms of linear matrix inequalities. The sufficient condition is derived by using mode-dependent Lyapunov function. In this step, two slack variables are inserted to make the proposed condition be necessary and sufficient condition in terms of strict linear matrix inequalities. Then, to prove the necessary condition, the positive real lemma for the hybrid system is proposed. Since the admissible singular system can be reformulated into stable normal system, the positive real lemma for the hybrid system holds. Thus, we give a necessary condition by constructing the solution of the proposed lemma from that of the hybrid systems.

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.

Exponential stability and interval stability of a class of stochastic hybrid systems driven by both Brownian motion and Poisson jumps

A class of stochastic singular hybrid systems driven by both Brownian motion and Poisson jumps are studied. This paper is devoted to discussing the exponential stability and interval stability of such stochastic singular hybrid systems. The concept of interval admissibility is proposed. Sufficient conditions are given for exponential mean square admissibility and interval admissibility by using Itô’s formula, H-representation and spectrum technique. Finally, two simulation cases are presented to demonstrate the theoretical results.

Delay-Dependent Stochastic Stability Analysis of Singular Hybrid System

The problem of Stochastic stability analysis for singular time-delay hybrid system with Markovian jumping parameters and standard Wiener process in this paper. Based on linear matrix inequality approach, a delay dependent condition is proposed, which ensures the singular hybrid system is stochastically stable.

Full-Order Disturbance-Observer-Based Control for Singular Hybrid System

The problem of the disturbance-observer-based control for singular hybrid system with two types of disturbances is addressed in this paper. Under the assumption that the system states are, unavailable, full-order observers (for both system states and the disturbance) and a nonlinear control scheme are constructed, such that the composite system can be guaranteed to be stochastically admissible, and the two types of disturbances can be attenuated and rejected, simultaneously. Based on the Lyapunov stability theory, sufficient conditions for the existence of the desired full-order disturbance-observer-based controllers are established in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the proposed approaches.

Stability of Singular Stochastic Systems With Markovian Switching

In recent years, singular hybrid systems have received considerable attention. However, few results are concerned with stability of singular hybrid stochastic systems. Based on a stability result for singular hybrid systems, this note studies mean-square stability of singular hybrid stochastic systems. It is found that the diffusions and the Markov chain may play important roles in system analysis in mean-square sense. As a special case, a criterion for mean-square stability of hybrid stochastic systems is developed by the frequency domain approach.

Solution of 2D singular hybrid linear system

PurposeThe purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.Design/methodology/approachComputation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.FindingsIn this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.Originality/valuePresented methods are a new way for computing the solution of singular 2D hybrid linear systems.

Stability and stabilization of continuous-time singular hybrid systems

In this paper, the problems of stability and state feedback stabilization for a class of continuous-time singular hybrid systems are investigated. A new sufficient and necessary condition for a continuous-time singular hybrid system to be regular, impulse-free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Moreover, a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

Control for discrete singular hybrid systems

The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach.