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53
Interconnected Automata and Linear Systems: A Theoretical Framework in DiscreteTime
 in Hybrid Systems III: Verification and Control
, 1996
"... . This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. 1 Introduction  The Need for Hybri ..."
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Cited by 51 (0 self)
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. This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. 1 Introduction  The Need for Hybrid Systems Linear control theory is welldeveloped and highly sophisticated, and is widely applied in areas ranging from aerospace to automotive control. Linear systems provide highly accurate models of many physical systems; furthermore, the use of linear systems as "robust" controllers often allows the tolerance of even severe model nonlinearities and uncertainties. However, it remains a fact that many continuous physical processes cannot be satisfactorily modeled linearly, nor can be adequately regulated by means of linear controllers alone. It has long been recognized that the control of more complex systems than those handled by the linear theory will require switching mechanisms (disco...
Input to state stability: Basic concepts and results
 Nonlinear and Optimal Control Theory
, 2006
"... The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification of classes of systems for which systematic decompositi ..."
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Cited by 46 (6 self)
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The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification of classes of systems for which systematic decomposition approaches can result in effective
The ISS philosophy as a unifying framework for stabilitylike behavior
 in Nonlinear Control in the Year 2000
, 2000
"... Abstract. The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results concerning ISS and related notions of input/output stability and detectability. A bibliography i ..."
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Cited by 44 (6 self)
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Abstract. The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results concerning ISS and related notions of input/output stability and detectability. A bibliography is also included, listing extensions, applications, and other current work. 1
Control of Linear Systems with Saturating Actuators
"... This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design. We take a semiglobal approach to solve some of the central control problems for such systems. These problems include: stabilization, inpu ..."
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Cited by 24 (4 self)
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This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design. We take a semiglobal approach to solve some of the central control problems for such systems. These problems include: stabilization, inputadditive disturbance rejection and robust stabilization in the presence of matched nonlinear uncertainties. We develop further the semiglobal design technology which was initiated in our earlier work [7] and utilize it to deal with these control problems.
On the Continuity and IncrementalGain Properties of Certain Saturated Linear Feedback Loops
 Proc. IEEE Conf. Decision and Control
, 1994
"... This paper discusses various continuity and incrementalgain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our previous ones, which applied to the same class of problems and provided finitegain stability. Keywords: satura ..."
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Cited by 19 (9 self)
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This paper discusses various continuity and incrementalgain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our previous ones, which applied to the same class of problems and provided finitegain stability. Keywords: saturatedinput linear systems, operator stability, finite incremental gain 1 Introduction
LowandHigh Gain Design Technique for Linear Systems Subject to Input Saturation  A Direct Eigenstructure Assignment Approach
 International Journal of Robust and Nonlinear Control
, 1994
"... The lowandhigh gain design technique, which was initiated in [10] for a chain of integrators and completed in [13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semiglobal control problems beyond stabilization and was related to the performan ..."
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Cited by 13 (7 self)
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The lowandhigh gain design technique, which was initiated in [10] for a chain of integrators and completed in [13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semiglobal control problems beyond stabilization and was related to the performance issues such as semiglobal stabilization with enhanced utilization of the available control capacity and semiglobal disturbance rejection. Although the lowandhigh gain design technique as initiated in [10] is based on explicit eigenstructure assignment, its full development in [13] is based on the solution of an algebraic Riccati equation (ARE) which is parameterized in an arbitrarily small scalar, called low gain parameter. In this paper, we develop a new complete lowand high gain design procedure which is based on explicit eigenstructure assignment. The new design approach avoids the solution of the numerically stiff parameterized ARE. Submitted to International Journal of Robust an...
Output Regulation For Linear Systems Subject To Input Saturation
, 1994
"... The purpose of this paper is to examine the problem of controlling a linear timeinvariant system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that a semiglobal framework for ..."
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Cited by 13 (9 self)
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The purpose of this paper is to examine the problem of controlling a linear timeinvariant system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that a semiglobal framework for this problem is a natural one. Within this framework, a set of solvability conditions are given and feedback laws which solve the problem are constructed. The theory developed in this paper incorporates earlier results established for linear systems without input saturation.
Global Asymptotic Controllability Implies Input to State Stabilization
, 2003
"... We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for full ..."
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Cited by 10 (8 self)
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We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for fully nonlinear GAC systems with actuator errors are also discussed.
Global analysis of piecewise linear systems using impact maps and quadratic surface Lyapunov functions: general theory. Submited for publication
 IEEE Transactions on Automatic Control
"... analysis, switching surfaces. In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global properties of PLS solely by studying their behavior at switching surfac ..."
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Cited by 10 (2 self)
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analysis, switching surfaces. In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global properties of PLS solely by studying their behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface, by constructing quadratic Lyapunov functions on switching surfaces. We found that an impact map induced by an LTI flow between two switching surfaces can be represented as a linear transformation analytically parameterized by a scalar function of the state. This representation of impact maps allows the search for quadratic surface Lyapunov functions to be done by simply solving a set of LMIs. Global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS can this way be efficiently checked. These new results were successfully applied to certain classes of PLS. Although this analysis methodology yields only sufficient criteria of stability, it has shown to be very successful in globally analyzing a large number of examples with a locally stable limit cycle or equilibrium point. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. 1
Reference Governor for Constrained Nonlinear Systems
, 1998
"... This note addresses the problem of satisfying pointwiseintime input and/or state hard constraints in nonlinear control systems. The approach is based on conceptual tools of predictive control and consists of adding to a primal compensated nonlinear system a Reference Governor (RG). This is a discr ..."
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Cited by 10 (2 self)
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This note addresses the problem of satisfying pointwiseintime input and/or state hard constraints in nonlinear control systems. The approach is based on conceptual tools of predictive control and consists of adding to a primal compensated nonlinear system a Reference Governor (RG). This is a discretetime device which online handles the reference to be tracked, taking into account the current value of the state, in order to satisfy the prescribed constraints. The resulting hybrid system is proved to fulfill the constraints, as well as stability and tracking requirements. I. Introduction In recent years the field of feedback control of dynamic systems with input and/or staterelated constraints has received considerable attention [1], [2]. Most of this research has addressed regulation problems for systems subject to input saturation. More recently, moving horizon optimal control [3], [4], [5] and model predictive control [6], [7] have been proved to be effective tools to deal with ...