Electrical and Electronic Engineering - Research Publications

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    A note on input-to-state stability of sampled-data nonlinear systems
    Teel, AR ; Nesic, D ; Kokotovic, PV (IEEE, 1998)
    It is shown for nonlinear systems that sampling sufficiently fast an input-to-state stabilizing (ISS) continuous time control law results in an ISS sampled-data control law. Two main features of our approach are: we show how the nonlinear sampled-data system can be modeled by a functional differential equation (FDE); we exploit a Razumikhin type theorem for ISS of FDE that was recently proved in [14] to analyze the sampled-data system.
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    Output stabilization of nonlinear systems: Linear systems with positive outputs as a case study
    Nesic, D ; Sontag, ED (IEEE, 1998)
    The problem of stabilization of linear systems for which only the magnitudes of outputs are measured is studied. A stabilizing controller is constructed which is input to state stability (ISS)-robust with respect to observation noise. Modal analysis and theorems are presented to prove the stabilization properties of the controller.
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    Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations
    Nesic, D ; Teel, AR ; Kokotovic, PV (ELSEVIER, 1999-12-10)
    Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.
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    Stabilizability and dead-beat controllers for two classes of Wiener-Hammerstein models
    Nesic, D ; Bastin, G (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-11)
    Two classes of block oriented models of the Wiener-Hammerstein type are considered. We prove that a generic condition is sufficient for a null controllable discrete-time system of this form to have a stabilizing minimum-time dead-beat controller. When the condition is violated, we show how to design a nonminimum time stabilizing (dynamic) dead-beat controller. The result is used to obtain stabilizability conditions for these systems.
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    Formulas relating K L stability estimates of discrete-time and sampled-data nonlinear systems
    Nesic, D ; Teel, AR ; Sontag, ED (ELSEVIER SCIENCE BV, 1999-09-15)
    We provide an explicit script K sign ℒ stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the script K sign ℒ estimate for the corresponding discrete-time system and a script K sign function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [1] or extend some results in [4] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.
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    Minimum phase properties for input nonaffine nonlinear systems
    Nesic, D ; Skafidas, E ; Mareels, IMY ; Evans, RJ (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-04)
    For input nonaffine nonlinear control systems, the minimum phase property of the system in general depends on the control law. Switching or discontinuous controllers may offer advantages in this context. In particular, there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are locally stable, whereas a discontinuous controller which achieves this exists. For single-input/single-output input nonaffine nonlinear systems we give sufficient conditions for existence and present a method for the design of discontinuous switching controllers which yield locally stable zero dynamics.
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    Controllability of structured polynomial systems
    Nesic, D ; Mareels, IMY (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-04)
    Two algorithms, based on the Grobner basis method, which facilitate the controllability analysis for a class of polynomial systems are presented. The authors combine these algorithms with some recent results on output dead-beat controllability in order to obtain sufficient, as well as necessary, conditions for complete and state dead-beat controllability for a surprisingly large class of polynomial systems. Our results are generically applicable to the class of polynomial systems in strict feedback form.
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    Controllability for a class of simple Wiener-Hammerstein systems
    Nesic, D (Elsevier, 1999-01-12)
    Controllability for a class of simple Wiener–Hammerstein systems is considered. Necessary and sufficient conditions for dead-beat and complete controllability for these systems are presented. The controllability tests consist of two easy-to-check tests for the subsystems.
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    Stabilisability and stability for explicit and implicit polynomial systems: A symbolic computation approach
    Nesic, D ; Mareels, IMY (SPRINGER-VERLAG LONDON LTD, 1999)
    Stabilisability and stability for a large class of discrete-time polynomial systems can be decided using symbolic computation packages for quantifier elimination in the first order theory of real closed fields. A large class of constraints on states of the system and control inputs can be treated in the same way. Stability of a system can be checked by constructing a Lyapunov function, which is assumed to belong to a class of polynomial positive definite functions. Moreover, we show that stability/stabilisability can be decided directly from the ε-δ definition.