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35
Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results
, 2005
"... During the last decade, there has been increasing interest in the stability analysis and switching control design for switched linear systems. This paper aims to briefly survey recent results in this field, focusing on stability analysis and switching stabilization problems. First, the stability an ..."
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Cited by 126 (10 self)
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During the last decade, there has been increasing interest in the stability analysis and switching control design for switched linear systems. This paper aims to briefly survey recent results in this field, focusing on stability analysis and switching stabilization problems. First, the stability analysis problem for switched linear systems is reviewed. We focus on the asymptotic stability analysis for switched linear systems under arbitrary switching, and highlight necessary and sufficient conditions for this problem. Secondly, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. One of the most elusive problems in the switched systems literature has been the switching stabilizability problem, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Necessary and sufficient conditions for asymptotic stabilizability of switched linear systems are described.
Rootmeansquare gains of switched linear systems
 IEEE Trans. Automat. Contr
, 2003
"... In this paper we compute the rootmeansquare (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant γ provides an upper bound on the RMS gain whenever there is a separation between the stabi ..."
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Cited by 26 (6 self)
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In this paper we compute the rootmeansquare (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant γ provides an upper bound on the RMS gain whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of γdependent algebraic Riccati equations. The motivation for this problem is the application of robust stability tools to the analysis of hybrid systems. 1
Robust stability and disturbance attenuation analysis of a class of networked control systems
 In Proc. of the 42th Conf. on Decision and Contr
, 2003
"... Abstract — In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H ∞ ..."
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Cited by 24 (4 self)
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Abstract — In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H ∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discretetime switched system. Then the NCSs ’ stability and performance problems can be reduced to corresponding problems for the switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discretetime switched systems and piecewise Lyapunov functions. I.
Quadratic Stabilizability Of Switched Linear Systems With Polytopic Uncertainties
 International Journal of Control
"... Abstract: In this paper, we consider quadratic stabilizability via state feedback for both continuoustime and discretetime switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. Fo ..."
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Cited by 23 (8 self)
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Abstract: In this paper, we consider quadratic stabilizability via state feedback for both continuoustime and discretetime switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuoustime switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discretetime switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of nonnegative scalars and a common positive definite matrix. For both continuoustime and discretetime switched systems, we propose the switching rules by using the obtained common positive definite matrix.
Linear parametrically varying systems with brief instabilities: an application to integrated vision/IMU navigation
 IEEE Trans. on Aerospace and Electronics Systems
, 2001
"... This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particula ..."
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Cited by 22 (10 self)
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This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particular type of complementary filters with guaranteed stability and performance in the presence of socalled outofframe events that arise when the vision system loses its target temporarily. The results obtained build upon new developments in the theory of linear parametrically varying systems (LPVs) with brief instabilities–also reported in the paper–and provide the proper framework to deal with outofframe events. Field tests with a prototype UAV illustrate the performance of the filter and the scope of applications of the new theory developed. Manuscript received January 10, 2003; revised December 14, 2003; released for publication April 12, 2004.
Disturbance attenuation properties for discretetime uncertain linear switched systems
 in Proceedings of the 42nd IEEE Conference on Decision and Control
, 2003
"... Abstract — In this paper, we study a class of discretetime switched linear systems affected by both parameter variations and additive l ∞ bounded disturbances. The problem of determining upper bounds on the l ∞ norm of the output is investigated. First, we study the condition under which the switch ..."
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Cited by 10 (5 self)
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Abstract — In this paper, we study a class of discretetime switched linear systems affected by both parameter variations and additive l ∞ bounded disturbances. The problem of determining upper bounds on the l ∞ norm of the output is investigated. First, we study the condition under which the switched systems have finite l ∞ induced gain. Secondly, the l ∞ induced gain is calculated for such switched system under arbitrary switching signals. Thirdly, we answer the question whether there exists proper switching mechanism for such switched system to achieve a given disturbance attenuation level. The techniques are based on positive invariant set theory. I.
Robust regulation of polytopic uncertain linear hybrid systems with networked control system applications
 Chapter in Contemporary Issues in Systems Stability and Control with Applications
, 2003
"... Abstract: In this chapter, a class of discrete time uncertain linear hybrid systems, affected by both parameter variations and exterior disturbances, is considered. The main question is whether there exists a controller such that the closed loop system exhibits desired behavior under dynamic uncerta ..."
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Cited by 6 (2 self)
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Abstract: In this chapter, a class of discrete time uncertain linear hybrid systems, affected by both parameter variations and exterior disturbances, is considered. The main question is whether there exists a controller such that the closed loop system exhibits desired behavior under dynamic uncertainty and exterior disturbances. The notion of attainability is introduced to refer to the specified behavior that can be forced to the plant by a control mechanism. We give a method for attainability checking that employs the predecessor operator and backward reachability analysis, and a procedure for controller design that uses finite automata and linear programming techniques. Finally, Networked Control Systems (NCS) are proposed as a promising application area of the results and tools developed here, and the ultimate boundedness control problem for the NCS with uncertain delay, package dropout and quantization effects is formulated as a regulation problem for an uncertain hybrid system.
A Necessary and Sufficient Condition for Robust Asymptotic Stabilizability of ContinuousTime Uncertain Switched Linear Systems
, 2004
"... The main contribution of this paper is a necessary and sufficient condition derived for the existence of asymptotically stabilizing switching laws for a class of switched linear systems with timevariant parametric uncertainties. This result improves upon the sufficient only conditions found in the ..."
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Cited by 4 (2 self)
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The main contribution of this paper is a necessary and sufficient condition derived for the existence of asymptotically stabilizing switching laws for a class of switched linear systems with timevariant parametric uncertainties. This result improves upon the sufficient only conditions found in the literature. The method is based on polyhedral Lyapunovlike functions, which represent generalizations of polytopic Lyapunov functions in the classical sense.
Stability and L2 gain analysis of discretetime switched systems
 Transactions of the Institute of Systems, Control and Information Engineers, Vol.15, No.3
"... Abstract: In this paper, we analyze stability and L2 gain properties for discretetime linear timeinvariant (LTI) systems controlled by a predesigned dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning c ..."
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Cited by 3 (3 self)
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Abstract: In this paper, we analyze stability and L2 gain properties for discretetime linear timeinvariant (LTI) systems controlled by a predesigned dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system’s stability and L2 gain properties are preserved to a desired level. For stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For L2 gain, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted L2 gain level, and the weighted L2 gain approaches normal L2 gain when the ATBCF is sufficiently large. KeyWords: Linear timeinvariant (LTI) system, dynamical output feedback, exponential stability, (weighted) L2 gain, controller failure, unavailability rate, average time between controller failures (ATBCF), piecewise Lyapunov function 1
Robust tracking and regulation control of uncertain piecewise linear systems
, 2003
"... Abstract: In this paper, a class of uncertain, discretetime, piecewise linear hybrid systems affected by both parameter variations and exterior disturbances is introduced. The robust tracking and regulation control problem for such uncertain piecewise linear hybrid systems is investigated. The main ..."
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Cited by 3 (1 self)
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Abstract: In this paper, a class of uncertain, discretetime, piecewise linear hybrid systems affected by both parameter variations and exterior disturbances is introduced. The robust tracking and regulation control problem for such uncertain piecewise linear hybrid systems is investigated. The main question is whether there exists a controller such that the closedloop system exhibits desired behavior under dynamic uncertainties and exterior disturbances. If a specified behavior can be forced on the plant by a control mechanism, then it is called attainable. We present a method for checking attainability that employs the predecessor operator and backward reachability analysis, and introduce a procedure for robust tracking and regulation controller design that uses linear programming techniques. This procedure is then used to solve the robust stabilization problem for uncertain piecewise linear hybrid systems.