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Stability analysis for class of switched nonlinear systems
No full textStability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. The results are illustrated by numerical examples
Optimal Filtering Scheme for Bilinear Discrete-Time Systems:a Linear Matrix Inequality Approach
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Frequency-Domain Generalized Singular Perturbation Method for Relative Error Model Order Reduction
Get PDFFrequency-Domain Balanced Stochastic Truncation for Continuous and Discrete Time Systems
No full textUdgivelsesdato: Jun
Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems
Get PDFThe notions of controllability and observability play an important role in different problems within feedback control analysis and design. To verify the controllability and observability of a system, several techniques have been introduced. However, often it is not only important to verify if the system is controllable or observable, but also it is required to know the degree of controllability or observability of the system. Gramian matrices were introduced to address this issue by providing a quantitative measure for controllability and observability. In many applications, the information on the controllability and observability properties of a system is needed within a specific frequency interval rather than the whole frequency-domain. The frequency interval gramians provide such information. While this concept were originally introduced for fixed known systems, it needs to be investigated for the case of uncertain systems. In this paper, we derive upper and lower bounds of frequency interval gramians under perturbations of an A-matrix in the state-space form. These bounds are obtained by solving algebraic Riccati equations. The results are further used to obtain upper and lower bounds of the frequency interval Hankel singular values for perturbed systems
Model Reduction of Hybrid Systems
Get PDFHigh-Technological solutions of today are characterized by complex dynamical models. Alot of these models have inherent hybrid/switching structure. Hybrid/switched systems arepowerful models for distributed embedded systems design where discrete controls are appliedto continuous processes. Hybrid systems are also an important modeling class for nonlinearsystems because a wide variety of nonlinearities are either piecewise-affine (e.g., a saturatedlinear actuator characteristic) or can be approximated as hybrid systems. The complexity ofverifying and assessing general properties of hybrid systems, designing controllers andimplementations is very high so that the use of these models is limited in applications wherethe size of the state space is large. To cope with complexity, model reduction is a powerfultechnique.This thesis presents methods for model reduction and stability analysis of hybrid/switchedsystems. Methods are designed to approximate hybrid/switched systems to low order modelswhich adequately describe the behavior of the switched systems. Three frameworks formodel reduction of switched systems are proposed which are based on the notion of thegeneralized gramians. Generalized gramians are the solutions to the observability andcontrollability Lyapunov inequalities. In the first framework the projection matrices arefound based on the common generalized gramians. This framework preserves the stability ofthe original switched system for all switching signals while reducing the subsystems of theswitched systems. The first framework is computationally efficient due to the construction ofa single projection for all subsystems. This framework is used for switched controllerreduction and it is shown that the stability of the closed loop system is guaranteed to bepreserved for arbitrary switching signal. To compute the common generalized gramianslinear matrix inequalities (LMI’s) need to be solved. These LMI’s are not always feasible. Inorder to solve the problem of conservatism, the second framework is presented. In thismethod the projection matrices are constructed based on the convex combinations of thegeneralized gramians. However this framework is less conservative than the first one, it doesnot guarantee the stability for all switching signals. The stability preservation is studied forthis reduction technique. The third framework for model reduction of switched systems isbased on the switching generalized gramians. The reduced order switched system isguaranteed to be stable for all switching signal in this method. This framework uses stabilityconditions which are based on switching quadratic Lyapunov functions which are lessconservative than the stability conditions based on common quadratic Lyapunov functions.The stability conditions which are used for this method are very useful in model reductionand design problems because they have slack variables in the conditions. Similar conditionsfor a class of switched nonlinear systems are derived in this thesis. The results are used foroutput feedback control of switched nonlinear systems. Model reduction of piecewise affinesystems is also studied in this thesis. The proposed method is based on the reduction of linearsubsystems inside the polytopes. The methods which are proposed in this thesis are applied toseveral numerical examples
Model Reduction of Hybrid Systems
Get PDFHigh-Technological solutions of today are characterized by complex dynamical models. Alot of these models have inherent hybrid/switching structure. Hybrid/switched systems arepowerful models for distributed embedded systems design where discrete controls are appliedto continuous processes. Hybrid systems are also an important modeling class for nonlinearsystems because a wide variety of nonlinearities are either piecewise-affine (e.g., a saturatedlinear actuator characteristic) or can be approximated as hybrid systems. The complexity ofverifying and assessing general properties of hybrid systems, designing controllers andimplementations is very high so that the use of these models is limited in applications wherethe size of the state space is large. To cope with complexity, model reduction is a powerfultechnique.This thesis presents methods for model reduction and stability analysis of hybrid/switchedsystems. Methods are designed to approximate hybrid/switched systems to low order modelswhich adequately describe the behavior of the switched systems. Three frameworks formodel reduction of switched systems are proposed which are based on the notion of thegeneralized gramians. Generalized gramians are the solutions to the observability andcontrollability Lyapunov inequalities. In the first framework the projection matrices arefound based on the common generalized gramians. This framework preserves the stability ofthe original switched system for all switching signals while reducing the subsystems of theswitched systems. The first framework is computationally efficient due to the construction ofa single projection for all subsystems. This framework is used for switched controllerreduction and it is shown that the stability of the closed loop system is guaranteed to bepreserved for arbitrary switching signal. To compute the common generalized gramianslinear matrix inequalities (LMI’s) need to be solved. These LMI’s are not always feasible. Inorder to solve the problem of conservatism, the second framework is presented. In thismethod the projection matrices are constructed based on the convex combinations of thegeneralized gramians. However this framework is less conservative than the first one, it doesnot guarantee the stability for all switching signals. The stability preservation is studied forthis reduction technique. The third framework for model reduction of switched systems isbased on the switching generalized gramians. The reduced order switched system isguaranteed to be stable for all switching signal in this method. This framework uses stabilityconditions which are based on switching quadratic Lyapunov functions which are lessconservative than the stability conditions based on common quadratic Lyapunov functions.The stability conditions which are used for this method are very useful in model reductionand design problems because they have slack variables in the conditions. Similar conditionsfor a class of switched nonlinear systems are derived in this thesis. The results are used foroutput feedback control of switched nonlinear systems. Model reduction of piecewise affinesystems is also studied in this thesis. The proposed method is based on the reduction of linearsubsystems inside the polytopes. The methods which are proposed in this thesis are applied toseveral numerical examples
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