Stable Subsystems Research Articles

Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach

This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions.

External stability of switching control systems

This paper investigates external stability (defined by the normal L2 norm) of switching control systems. It proposes definitions of the maximum, minimum dwell time for switching systems and then derives an important relation between the number of switchings and the maximum, minimum dwell time. Applying this relation, it establishes criteria on external stability of switching control systems consisting of Hurwitz stable subsystems. Furthermore, a switching law is proposed, and is proven to be realizable. Given this proposed switching law and applying the previous derived relation, the switching control systems comprised of both Hurwitz stable and Hurwitz unstable subsystems are proved to be externally stable.

New Results on Stability of Slowly Switched Systems: A Multiple Discontinuous Lyapunov Function Approach

In this technical note, the problem of stability for a class of slowly switched systems is investigated. By developing a novel multiple discontinuous Lyapunov function approach and exploring the feature of mode-dependent dwell time switching, new stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems. In particular, stability conditions for linear switched systems are also given via choosing multiple discontinuous Lyapunov functions in the quadratic form. Moreover, stability criteria for the systems consisting of stable subsystems are also derived. It is shown that our proposed results cover some existing ones in literature as special cases, and provide tighter bounds on the dwell time. Finally, some simulation results are provided to show the advantages of the theoretic results obtained.

VSC-HVDC system robust stability analysis based on a modified mixed small gain and passivity theorem

In a VSC-HVDC system, when the input power to the converter is controlled to a positive constant, the converter acts a differential negative resistance — Po/i20, which may cause instability in case of a connected weak AC-grid. In order to analyze the robust stability of such a system, a modified mixed small gain and passivity theorem is proposed, which shows that the negative feedback interconnection of two linear time invariant stable subsystems (converter admittance and AC-grid impedance) is input to output stable if in certain frequency bands, both subsystems are passive and at least one of them is strictly passive; at the remaining frequency bands, the loop gain is to be strictly less than one. Under different AC-grid topologies, the stability sufficient conditions with respect to the AC-grid inductance are studied. It shows that for AC-grid consists of series RgLg-circuit, an introduced series capacitor can improve the system robustness but not for the shunt capacitor.

Impedance-Sum Stability Criterion for Cascaded Power Electronic Systems

: The impedance-ratio criterion has been widely adopted to analyze the stability of cascaded power electronic systems. However, for different cascaded systems, the impedance ratio takes different forms. For cascaded systems with a voltage-controlled source, it is the ratio of the output impedance of the source converter to the input impedance of the load converter. For cascaded systems with a current-controlled source, it is the ratio of the input impedance of the load converter to the output impedance of the source converter. In this paper, a generic stability criterion in terms of the sum of the impedances of individual subsystems is proposed. A cascaded system with individually stable subsystems is stable if and only if the sum of the impedances of the subsystems does not encircle the origin clockwise or equivalently the impedance sum does not have right-half-plan (RHP) zeros. Real-time simulation results are presented to validate this generic stability criterion.

H∞ Filtering for a class of nonlinear switched systems with stable and unstable subsystems

This paper studies the H∞ filtering problem for a class of nonlinear switched systems with stable and unstable subsystems. The Takagi–Sugeno (T–S) fuzzy model is used to approximate each nonlinear subsystem. Using the T–S fuzzy model, the nonlinear switched systems are modeled into the switched T–S fuzzy systems. To guarantee the designed filters can correctly estimate the output of switched systems with unstable subsystems, a set of mode-dependent filters of a Luenberger-like observer type is constructed. In contrast to the filtering error system constructed by the augmentation technique, the filtering error system considered in our work does not contain any unstable filtering error subsystems even with the existence of unstable subsystems in switched systems. The multiple Lyapunov functions approach and the mode-dependent average dwell time technique are employed to solve the H∞ filtering problem. New sufficient conditions for the existence of H∞ filters for the switched T-S fuzzy systems with unstable subsystems are developed. The obtained results can ensure the filtering error system to be asymptotically stable with a prescribed H∞ performance index and have less computational burden. Moreover, the desired H∞ filters can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given.

Finite-Time Stability for Networked Switched Control Systems with Not Finite-Time Stable Subsystems

In this paper, we studied finite-time stability for a class of Networked Switched Control Systems (NSCSs) with time-delays and uncertainties and its subsystems are not finite-time stable. At the beginning, the concepts of Average Dwell Time (ADT), finite-time stability and uniformly finite-time stability of NSCSs are given by 3 definitions. Then sufficient conditions are given under which networked switched linear control systems with subsystems that are not finite-time stable can changed to be finite-time stable. Finally, numerical examples are employed to verify the efficiency of the proposed methods.

Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems

This paper discusses the asymptotic stability of Markov switched stochastic differential equations. By using the method of multiple Lyapunov functions, we provide sufficient conditions for stochastic asymptotic stability of Markov switched stochastic differential equations with both stable and unstable subsystems via the inequality based on the multiple Lyapunov functions and the stationary distribution of Markovian switching process. Particularly, our results include some existing results as special cases and improve some results in the literature. Two examples are given to illustrate the effectiveness of the obtained results.

Improved adaptive backstepping sliding mode control for generator steam valves of non‐linear power systems

The stability problem of steam valves in a single machine infinite bus system with thyristor controlled series compensation is addressed through the use of an improved adaptive backstepping method based on error compensation. The method combines sliding mode variable structure control, backstepping control and adaptive control. Initially, an excitation control input and error compensation are simultaneously obtained in the design of virtual control by adaptive backstepping and the Lyapunov method. The Lyapunov function is then constituted in stages to achieve subsystem stability, before obtaining a parameter updating law and a non-linear control law for the closed-loop system. The results for both systems show that the improved non-linear backstepping sliding mode variable structure control approach can have four benefits. It can ensure that the system states are bounded, retain the faster stability of power systems, improve the speed of parameter identification and achieve real-time parameter estimation. Finally, a simulation is presented to illustrate both the effectiveness and the feasibility of the improved control approach.

Sampled-data state estimation for a class of delayed complex networks via intermittent transmission

This paper investigates the sampled-data state estimation problem for a class of delayed complex networks. At certain sampling times, transmission of sampled-data through communication network may fail, which means the considered estimator can only intermittently receive sampled-data. The main objective of this paper is to design a sampled-data state estimator subjected to intermittent transmission such that the error system is exponentially stable. Specifically, the error system is first transformed into time-varying delayed switched systems, including both stable and unstable subsystems. And then, to analyze the stability of the error system, a modified Halanay inequality is presented. In view of the modified Halanay inequality and switched systems methodology, a sufficient condition for globally exponential stability of the error system is established. Meanwhile, the upper bound of transmission failure rate is given, which reflects to be closely related to sampling period and the upper bound of node delays. Furthermore, the desired estimator gain of each node is explicitly provided by solving a set of matrix inequalities. Finally, a numerical simulation is carried out to verify the effectiveness of the inferred results.

Stability and asynchronous stabilization for a class of discrete-time switched nonlinear systems with stable and unstable subsystems

The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained.

Infant-Guided, Co-Regulated Feeding in the Neonatal Intensive Care Unit. Part II: Interventions to Promote Neuroprotection and Safety.

Feeding skills of preterm neonates in a neonatal intensive care unit are in an emergent phase of development and require careful support to minimize stress. The underpinnings that influence and enhance both neuroprotection and safety were discussed in Part I. An infant-guided, co-regulated approach to feeding can protect the vulnerable neonate's neurologic development, support the parent-infant relationship, and prevent feeding problems that may endure. Contingent interventions are used to maintain subsystem stability and enhance self-regulation, development, and coping skills. This co-regulation between caregiver and neonate forms the foundation for a positive infant-guided feeding experience. Caregivers select evidence-based interventions contingent to the newborn's communication. When these interventions are then titrated from moment to moment, neuroprotection and safety are fostered.

Marginally stable and turbulent boundary layers in low-curvature Taylor–Couette flow

Marginal stability arguments are used to describe the rotation number dependence of torque in Taylor–Couette (TC) flow for radius ratios $\unicode[STIX]{x1D702}\geqslant 0.9$ and shear Reynolds number $\mathit{Re}_{S}=2\times 10^{4}$. With an approximate representation of the mean profile by piecewise linear functions, characterised by the boundary-layer thicknesses at the inner and outer cylinder and the angular momentum in the centre, profiles and torques are extracted from the requirement that the boundary layers represent marginally stable TC subsystems and that the torque at the inner and outer cylinder coincide. This model then explains the broad shoulder in the torque as a function of rotation number near $R_{\unicode[STIX]{x1D6FA}}\approx 0.2$. For rotation numbers $R_{\unicode[STIX]{x1D6FA}}<0.07$ the TC stability conditions predict boundary layers in which the shear Reynolds numbers are very large. Assuming that the TC instability is bypassed by some shear instability, a second narrower maximum in torque appears, in very good agreement with numerical simulations. The results show that marginal stability theory, despite its shortcomings in other cases, can explain quantitatively the non-monotonic torque variation with rotation number for both the broad maximum as well as the narrow maximum.

Dwell-time-based stabilization of switched linear singular systems with all unstable-mode subsystems

The global stabilization design of a class of switched linear singular systems via a novel dwell-time switching is investigated and solved in this work. The distinguishing feature of the proposed method is that stability of all subsystems of the switched systems is not necessarily required. A time-varying coordinate transformation is introduced first in order to convert the problem into an equivalent one of reduced-order switched conventional linear system with state jumps. Then, by constructing certain new multiple time-varying Lyapunov functions, computable sufficient conditions for the global stabilization task are proposed within the framework of dwell-time switching. Given the assumed instability of individual subsystems, the stabilization of the switched system is achieved under the condition of confining the dwell time by a certain pair of upper and lower bounds, which restrict the growth of Lyapunov function for the actively operating subsystem, thus decrease the energy of the Lyapunov function of the overall switched system at switching times. In addition, the multiple time-varying Lyapunov functions method is also used to analyze the stability analysis of a class of switched linear singular systems with stable subsystems. Two illustrative examples are presented to demonstrate the effectiveness of the proposed method.

Finite-Time Stabilization of Discrete-Time Switched Nonlinear Systems Without Stable Subsystems via Optimal Switching Signal Design

This paper investigates the finite-time exponential stability analysis and stabilization problem of discrete-time switched nonlinear systems without stable subsystems. In the stability analysis, the Takagi–Sugeno (T–S) fuzzy model is employed to approximate nonlinear subsystems. With two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce switched fuzzy systems with approximation errors, which inherently contain both the features of the switched systems and T–S fuzzy systems. By constructing the “decreasing-jump” piecewise Lyapunov-like functions and minimum dwell time technique, a finite-time exponential stability of switched fuzzy systems with bounded approximation errors is obtained. Then, based on the finite-time exponential stability, a multiobjective evolution algorithm (nondominated sorting genetic algorithm, NSGA-II), which considers two conflicting objectives, such as the average convergence error and the average switching cost, is proposed to generate tradeoff switching sequences to stabilize the discrete-time switched nonlinear systems over a finite-time interval. A numerical example and a practical example are provided to illustrate the effectiveness of the stability and the algorithm, respectively.

Assessment of Sustainability and Environmental Balance Level of a Region (Case study of Poltava Region)

Objective: assessment of sustainability and level of environmental balanced development of the Poltava region with justification of approach to the choice of estimated indicators. Methods: a quantitative and qualitative analysis and synthesis, methods of classification and correlation analysis. Results: researched of existing approaches to defining parameters, indexes and indicators related to sustainable development. Chosen and reviewed method for assessment of environmental sustainability and sustainable development proposed by Harmut Bossel. The systematization of indicators and the estimation of sustainability on 14 indicators for Poltava region according to the methodology of Harmut Bossel. Based on the chosen indicators were built “guiding star”, which give a clear understanding of the dynamics of change in each of the subsystems, level of its stability and potential of subsystem to restore. Conclusions: in general, the results of the evaluation according to the methodology of Harmut Bossel showed overall instability of the ecological system of the Poltava region, which is typical for the entire investigated period (2005–2015 years). Based on the evaluation, defined the priority environmental problems that are «weak links» of ecological system and which require urgent focusing, that ensuring gradual stabilization processes in the environmental development of the region.

Methods of search for stable solutions of some optimization problems in the theory of recognition by precedents

In constructing some models of recognition algorithms, there arise a number of optimization problems. The search for the optimal consistent subsystem of a given system of linear inequalities plays an important role in the process of data analysis in the theory of recognition by precedent. The optimality of a required subsystem is defined by a number of the conditions imposed on it. Earlier the author developed several algorithms for solving the problems of this type. These algorithms are based on exhaustive search for nodal subsystems of a given system of linear inequalities. In the search for optimal consistent subsystem, these algorithms find boundary decisions. However, in practical application often it is necessary to find a stable solution. So, when looking for logical regularities of a special type, it is required to find a set of non-degenerate polyhedra describing a certain class of objects in a space of features. Therefore, linear inequalities systems corresponding to these polyhedra must be stable. In this paper, we propose a method for modifying the previously developed algorithms to select the stable consistent subsystem of highest possible power and find its stable solution.

Exponential Stability of Switched Positive Homogeneous Systems

This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. In order to capture the decay rate of such systems, we first consider the subsystems. A sufficient condition for exponential stability of subsystems with time-varying delays is derived. In particular, for the corresponding delay-free systems, we prove that this sufficient condition is also necessary. Then, we present a sufficient condition of exponential stability under minimum dwell time switching for the switched positive nonlinear systems. Some results in the previous literature are extended. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.

Stability Analysis for Discrete-Time Switched Nonlinear System Under MDADT Switching

The problem of stability analysis for discrete-time switched nonlinear system is investigated with mode-dependent average dwell time (MDADT) method in this paper. A slow switching strategy is adopted in the discrete-time nonlinear stable subsystems and unstable subsystems are handled by a fast switching strategy. Takagi-Sugeno (T-S) fuzzy model is utilized to approximate the switched nonlinear system. By constructing a multiple discontinuous Lyapunov function approach, the stability condition of switched T-S fuzzy system is built to get tighter bound on MDADT, which shows that our proposed method outperforms the classical one. Finally, through a numerical example, the effectiveness of the presented control approach is illustrated by comparison with result from classical one.

Stability analysis and stabilization synthesis of singularly perturbed switched systems: An average dwell time approach

Stability analysis and stabilization synthesis problems of the singularly perturbed switched systems (SPSSs) are investigated in this paper. First, stability of the SPSS with stable subsystems is discussed by using an average dwell time approach with a full-order piecewise Lyapunov function. Then, the result is extended to the situation that not all the subsystems are Hurwitz stable. Furthermore, state feedback controllers are designed when all subsystems are stabilizable, and the design method is extended to the situation that not all subsystems are stabilizable. Finally, two examples are given to demonstrate the validity and effectiveness of the proposed methods.