Search

This study investigates the H∞ control problem for a class of continuous-time Markovian jump singular systems. The authors' attention is focused on the design of state and static output feedback controllers which ensure that the closed-loop system is regular, impulse-free and stochastically stable, and satisfies a prescribed H∞ performance level. To investigate the problem of H∞ performance analysis for the system under consideration, a bounded real lemma (BRL) is provided in terms of linear matrix inequality (LMI) containing equality constraints, which may not be a problem from the theoretical point of view, but may cause great big trouble in checking the conditions numerically. To solve this problem, a new version of BRL is also provided in terms of strict LMIs. Based on this, two approaches are established to solve the problem of state feedback H∞ control, and then, the problem of static output feedback H∞ control is solved, which can also be used for solving the dynamic output feedback control problems. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

In this paper, we consider the discrete-time mixed ℋ2/ℋ∞ filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite-dimensional filter are given in terms of a pair of coupled discrete-time Hamilton–Jacobi-Isaac's equations (DHJIE) with some side-conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete-time algebraic-Riccati-equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite-horizon and infinite-horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.

The stochastic stability and robust stochastic stabilisation for time-delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on stochastic Lyapunov functional, a delay-dependent linear matrix inequalities (LMIs) condition for the time-delay discrete Markovian jump singular systems to be regular, causal and stochastically stable is given. With this condition, the problem of robust stochastic stabilisation is solved. A numerical example to illustrate the effectiveness of the method is given.

A class of extended continuous-time Markov jump linear systems is proposed in this study. The generality lies in that the discrete dynamics of the class of systems is described by a Markov stochastic process, but with only partially known transition probabilities, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be known a priori. Moreover, in contrast with the uncertain transition probabilities studied recently, no structure (polytopic ones), bounds (norm-bounded ones) or ‘nominal’ terms (both) are required for the partially unknown elements in the transition rate matrix. The sufficient conditions for H∞ control are derived via the linear matrix inequality formulation such that the closed-loop system is stochastically stable and has a guaranteed H∞ noise-attenuation performance. A tradeoff can be built using our approach between the difficulties to obtain all the transition probabilities and the systems performance benefits. A numerical example is provided to show the validity and potential of the developed theoretical results.

In this paper, a new theory of two-degrees-of-freedom (2-DOF)-ℋ∞ and certainty-equivalent filters is presented. Exact and approximate solutions to the nonlinear ℋ∞ filtering problem using this class of filters are derived in terms of discrete-time Hamilton–Jacobi–Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree-of-freedom, these filters are a substantial improvement over the earlier 1-DOF case. The theory presented is also generalized to n-DOF filters, which bore strong connections to linear infinite-impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach. Copyright © 2009 John Wiley & Sons, Ltd.

The problem of the stability and stabilization of Markov jumping singular systems with discontinuities and saturating inputs is addressed. The design procedure via linear matrix inequality technique (LMI) and the sequential linear programming matrix method (SLPMM) are used to determine simultaneously a state feedback control and an associated domain of safe admissible states for which the regularity, the absence of impulsive behavior and the stochastic stability in the mean square sense of the closed-loop systems are guaranteed. A numerical example is provided to demonstrate the effectiveness of the proposed methods.

The robust H∞ filtering problem for mode-dependent time-delay discrete Markov jump singular systems with parameter uncertainties is discussed. Based on delay-dependent linear matrix inequalities, a Markov jump filter is designed, which guarantees that the filtering error system is regular, causal, stochastically stable and satisfies H∞ performance for all admissible uncertainties. The H∞ filter can be of full or of a reduced order. A numerical example is given to illustrate the effectiveness of the proposed method.

In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory.

This paper deals with the class of uncertain continuous-time linear stochastic hybrid systems with Wiener process. The uncertainties that we are considering are of the norm-bounded type. The robust \({\cal {H}}_{\infty}\) stochastic stabilization problem is treated. LMIs based sufficient conditions are developed to design the state feedback controller that robustly and stochastically stabilizes the studied class of systems and at the same time rejects a disturbance of desired level. The minimum disturbance rejection is also determined. A numerical example is provided to show the validity of the proposed results.

This paper deals with the uncertain class of continuous-time linear systems with Markovian jumping parameters and multiplicative Brownian disturbance. A design method for a nonfragile robust controller for this class of systems is proposed when the uncertainties are of the norm-bounded type. An LMI based sufficient condition is developed. The methodology used is based mainly on the Lyapunov approach. A numerical example is presented to show the usefulness of the proposed results.

This paper deals with the uncertain class of continuous-time linear systems with Markovian jumping parameters. A design method for a nonfragile robust controller for this class of systems is proposed when the uncertainties in the system matrices are of the norm-bounded type. An LMI based sufficient condition is developed. The methodology used is based mainly on the Lyapunov approach. A numerical example is presented to show the usefulness of the proposed results.

This paper considers the stabilization problem of the class of continuous-time linear stochastic hybrid systems with Wiener process. Theℋ∞state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI-based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.

This paper deals with the class of continuous-time linear systems with Markovian jumps and multiple time delays. The systems that we are treating are assumed to have time-varying delays in their dynamics which can be different and also have uncertainties in the system parameters. The time-varying structure of the bounded uncertainties is considered. Delay-dependent conditions for stochastic stability and stochastic stabilizability and their robustness are considered. A design algorithm for a stabilizing memoryless controller is proposed. All the results are given in the LMI formalism.

This paper studies the class of uncertain linear systems with time delay and Markov jump disturbance, in which the time delay is assumed to be dependent on the system mode. An LMI-based condition for this class of systems to be robustly stable is established. Sufficient conditions for the robust stabilizability under a state feedback controller are developed, and an LMI-based method to design the state feedback is proposed. Numerical examples are worked out to show the usefulness of the theoretical results.

This paper deals with the production planning problem for discrete-time manufacturing systems with deteriorating items. A minimax approach is presented throughout the paper for the case where the demand is unknown. Both the cases of finite horizon and infinite horizon are discussed. Moreover, the case of production planning for manufacturing systems with failure-prone machines is also considered. For this case, a stochastic approach is used in which the states of the machines are represented by a two-state Markov process with transition rates determined by the availability of the machines. Finally, a robust control policy to take care of plant uncertainties is developed. Simulation results are also presented to show the usefulness of the approaches.

Studies the problem of Kalman filtering for a class of uncertain linear continuous-time systems with Markovian jumping parameters. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in the state and measurement equations. Stochastic quadratic stability of the above system is analyzed. A state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties, which is in terms of solutions of two sets of coupled algebraic Riccati equations.

This paper studies the problem of control for discrete time delay linear systems with Markovian jump parameters. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and unknown time delay in the state, and Markovian jump parameters in all system matrices. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution.

In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem.

This paper deals with the mean square stochastic stability of the class of linear time-delay systems with Markovian jumping parameters. A delay-independent sufficient condition for checking the stochastic stability of this class of systems is established. A numerical example is given to show the usefulness of the proposed theoretical results.

This paper studies the problem of H∞-control for linear systems with Markovian jumping parameters. The jumping parameters considered here are two separable continuous-time, discrete-state Markov processes, one appearing in the system matrices and one appearing in the control variable. Our attention is focused on the design of linear state feedback controllers such that both stochastic stability and a prescribed H∞-performance are achieved. We also deal with the robust H∞-control problem for linear systems with both Markovian jumping parameters and parameter uncertainties. The parameter uncertainties are assumed to be real, time-varying, norm-bounded, appearing in the state matrix. Both the finite-horizon and infinite-horizon cases are analyzed. We show that the control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of coupled differential Riccati equations for the finite-horizon case or algebraic Riccati equations for the infinite-horizon case. Particularly, robust H∞-controllers are also designed when the jumping rates have parameter uncertainties.

This paper deals with the robustness of the class of nonlinear systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption that the Markovian jump process (disturbance) is irreducible and under complete access to the system state and its mode, we establish robust stability results in two cases: (i) under matching conditions; and (ii) under bounded uncertainties.

Consider a model of a flexible rnanufacturing system with failure-prone machines. The control variables are the rates of maintenance, repair, and production. The objective is to choose these control variables over time that minimize the total cost of over/under stock, repair, and maintenance with either discounted cost or average cost per unit time. The focus of this work is on the modeling and numerical methods for a wear process formulation. A Markov chain approach is used to deal with the approximation problem. The dynamic programming equation is used only for suggesting a good numerical approximation scheme. The convergence result is obtained by deriving the weak convergence of the associated Markov chain. A one machine one part type model is given as an illustration for the numerical experiment

This paper deals with the asymptotical stability problem for a class of feedforward nonlinear systems with delays in the state and input. The uncertainties in the systems are assumed to be dominated by upper polynomial functions multiplying by an incremental rate depending on the input or delayed input. Based on the state transformation of nonlinear systems and the Lyapunov method, both linear state feedback and linear output feedback controllers with dynamic low gains are provided. The theoretical results are illustrated with an academic example.

This paper deals with the class of continuous-time linear Markovian jumps singular systems with discontinuities. Based on the Lyapunov method, a design procedure for an output feedback controller, via the linear matrix inequality (LMI) technique and the sequential linear programming matrix methods (SLPMM), is proposed for this class of systems. A numerical example is presented to show the usefulness of the proposed results.

In this paper, we consider the problem of designing an observer-based output feedback controller for the class of Markovian jump bilinear descriptor systems (MJBDS). First, we investigate the existence and the uniqueness of the solution, then we derive sufficient conditions that guarantee the regularity, absence of impulses and stochastic stability in asymptotic mean-square sense of the closed-loop system. Based on linear matrix inequality approach (LMI), all results are expressed in terms of a set of strict LMIs, which are more reliable in numerical computation. A numerical example is provided to demonstrate the applicability of the proposed approach.

In this paper, we investigate the regulation problem for linear discrete-time delay systems with Markovian jumps and constrained control. The constraints used here are of non symmetrical inequality type. A sufficient condition of stochastic stability of a closed loop system is derived. We use the positive invariance approach of the common set for all the modes to guarantee the admissibility of the control law. In the case of one mode, we obtain the condition of stability for a linear discrete-time delay system as known in the literature. A numerical example is given to illustrate the theoretic results.

This paper considers the problem of designing an observer-based output feedback controller for the class of continuous-time linear singular systems with Markovian jumping parameters. The objective is to find an observer-based controller that guarantees the stochastic stability of the closed-loop system. Sufficient conditions for solvability of this problem are obtained and a characterization of the controller is given in terms of the solutions of linear matrix inequalities. A numerical example is presented to show the usefulness of the proposed results.

Consider the production of a single consumable product that is fabricated in a process of k stages that is subject to an uncertain environment. There are a number of workstations on each stage that have different operating parameters. The workstations are subject to the discrete events of repair, failure, and preventive maintenance that generate a jump in the state of the system. Between each stage of the manufacturing process is a finite buffer that holds pieces before they can be processed by the next stage. If a buffer is full, then the preceding stage cannot produce pieces since there will be no place for them to go. This formulation of a manufacturing system is a hybrid system consisting of the meeting the global production demand while locally managing the operational status of the workstations. This formulation of the optimal scheduling of production is a quasi-LQGP problem whose jumps are generated by state dependent Poisson processes. A numerical example is presented to illustrate the model.

This paper studies the problem of control for discrete time-delay linear systems with Markovian jump parameters. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time-delay.

This paper deals with the class of uncertain continuous-time linear systems with Markovian jumps, time-delay, and saturating actuators. Under norm-bounded uncertainties and based on the Lyapunov method, a sufficient condition on stochastic stability and stochastic stabilizability are developed. A design algorithm for a stabilizing observer-based robust output feedback controller is proposed in terms of the solutions of linear matrix inequalities (LMIs).

In this paper, we investigate the regulation problem for linear discrete-time delay sustems with Markovian jumps and constrained control. The constraints used hete are of symmetrical inequality type. A sufficiemt condition of stochastic stability of closed loop sustem is derived. We use the positive invariance approach of the common set for all the modes to guarntee the admissibility of the control law. In the case of one mode, we obtain the condition of stability for a linear discrete-time delay system as known in the literature. A numerical example is given to ukkustrate the theoretic results.

We study the problems of stability and stability robustness for a class of discrete-time linear systems with Markovian jumping parameters (DTLSMJP) with norm bounded uncertainties. A necessary and sufficient condition for stochastic stability is established using a Lyapunov exponent. The approach gives a direct expression of the second moment that allows us to conclude on the stochastic stability of the DTLSMJP in the mean-square sense. Under the assumption that the uncertainties are norm bounded a sufficient condition guaranteeing the robust stability of the uncertain discrete-time linear systems with Markovian jumping parameters (UDTLSMJP) is presented, and it is in terms of a set of coupled discrete-time algebraic Riccati equations.

We investigate the H/sub /spl infin// control problem for a class of linear discrete-time systems with Markovian jumping parameters. The jumping parameters considered is modelled by a discrete-time Markov process. Our attention is focused on the design of linear state feedback controller such that both stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved when the real system under consideration has different types of uncertainties. Sufficient conditions, which are in terms of a set of solutions of coupled algebraic Riccati inequalities, are proposed to solve the above problem.

We study the problem of robust stabilizability of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). Under the assumption of complete access to the continuous state, the stochastic stabilizability of the nominal system and the boundedness of the system's uncertainties, sufficient conditions which guarantee the robust stability of the uncertain systems are presented, which are in terms of a set of coupled algebraic Riccati equations.