- D. Chatterjee, A. Patra, and H. K. Joglekar, Swing-up and
stabilization of a cart-pendulum system under restricted cart track
length Systems & Control Letters, Vol. 47, No. 4,
pp 353-362, Nov, 2002.
[Abstract: This paper describes the swing-up and stabilization of a cart pendulum system with a restricted cart track length and restricted control force using generalized energy control methods. Starting from a pendant position, the pendulum is swung up to the upright unstable equilibrium configuration using energy control principles. An ``energy well'' is built within the cart track to prevent the cart from going outside the limited length. When sufficient energy is acquired by the pendulum, it goes into a ``cruise'' mode when the acquired energy is maintained. Finally, when the pendulum is close to the upright configuration, a stabilizing controller is activated around a linear zone about the upright configuration. The proposed scheme has worked well both in simulation and a practical setup and the conditions for stability have been derived using the multiple Lyapunov functions approach.]
- D. Chatterjee and D. Liberzon, Stability analysis of
deterministic and stochastic switched systems via a comparison
principle and multiple Lyapunov functions, SIAM Journal on Control
and Optimization, vol. 45, no. 1, pp. 174-206, 2006.
[This article may be found here. Typos
]
[Abstract: This paper presents a general framework for analyzing stability of nonlinear switched systems, by combining the method of multiple Lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures. For deterministic switched systems, this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple Lyapunov functions. For switched systems perturbed by white noise, we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones. In particular, we study stability of deterministic and stochastic switched systems under average dwell-time switching.] - L. Vu, D. Chatterjee, and D. Liberzon, Input-to-state
stability of switched systems and switching adaptive control. (
Automatica, vol. 43, pp. 639-646, April 2007) [This article may be found here.]
[Abstract: In this paper we prove that a switched nonlinear system has several useful ISS-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.] - D. Chatterjee and D. Liberzon, Stability of Randomly
Switched Systems. (To appear in IEEE Transactions on Automatic
Control) [Preprint may be found here.]
[Abstract: This article is concerned with stability analysis and stabilization of randomly switched systems. These systems may be regarded as piecewise deterministic stochastic systems; the discrete switchings are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure and mean stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markovian jump systems in particular. For systems with control inputs we provide explicit control schemes for stabilization.] - D. Chatterjee and D. Liberzon, Stabilizing Randomly Switched Systems. (To be submitted to SICON)
[Abstract:
This article is concerned with stability analysis and stabilization of
randomly switched systems with control inputs. The switching signal is
modeled as a jump stochastic semi-Markov process independent of the system state;
it selects, at each instant of time, the active subsystem from a family
of systems. We first establish sufficient conditions for stochastic
stability of the switched system when the subsystems
do not possess control inputs; not every subsystem is required to be
stable. Thereafter we design feedback controllers when the
subsystems are affine in control, the control space being general
subsets of 
. Our analysis results and universal
formulae for
feedback stabilization of nonlinear systems for the corresponding
control spaces constitute the primary tools for control design.]
. Our analysis results and universal
formulae for
feedback stabilization of nonlinear systems for the corresponding
control spaces constitute the primary tools for control design.]- D. Chatterjee and D. Liberzon, Randomly Switched Systems: External Stability and Stabilization. (Preprint)
[Abstract:
This article is concerned with stability analysis and stabilization of
randomly switched systems with control inputs in the presence of
disturbances. The switching signal is
modeled as a jump stochastic process independent of the system state;
it selects, at each instant of time, the active subsystem from a family
of systems. A class of switching signals whose holding times and values
at jump instants are mutually independent i.i.d sequences is
considered. We first establish sufficient conditions for stochastic
versions of input to state stability (ISS) of the switched system when
the subsystems
do not possess control inputs; not every subsystem is required to be
stable. Thereafter we design feedback controllers when the
subsystems are affine in control, the control space being general
subsets of . Our analysis results and universal
formulae for ISS-disturbance attenuation of nonlinear systems for the
corresponding
control spaces constitute the primary tools for control design.]
. Our analysis results and universal
formulae for ISS-disturbance attenuation of nonlinear systems for the
corresponding
control spaces constitute the primary tools for control design.]- H. K. Joglekar, D. Chatterjee, A. Patra, Swing-up
and stabilization of a cart-pendulum system using energy control in
Proceedings of International Conference on Energy, Automation and
Information Technology, Department of Electrical Engineering, IIT
Kharagpur, Dec 10-12, 2001, pp 33-37.
[Abstract: This paper describes the swing-up and stabilization of a cart-pendulum system with restricted cart-length and restricted control force using energy methods. The pendulum starts from the inverted position which is the stable equilibrium position and swing-up is achieved using energy-control. After the pendulum acquires sufficient energy to reach the upright position the control is switched to a throwing strategy. The pendulum then swings freely until it reaches the upright equilibrium position which is the unstable equilibrium position. Here control is switched to the stabilizing strategy which then stabilizes it in the upright position. It is observed that ``throwing'' plays a very significant role in the ultimate stabilization of the system because throwing has to be done at the moment the total pendulum energy reaches the value at the upright position.] - D. Chatterjee and D. Liberzon, On stability of
stochastic switched systems, in Proceedings of the 43rd Conference
on Decision and Control, Paradise Island, Bahamas, Dec 2004,
pp. 4125-4127. [The article may be found here.]
[Abstract: This paper proposes a method for stability analysis of switched systems perturbed by a Wiener process. It utilizes multiple Lyapunov-like functions and is analogous to an existing result for deterministic switched systems.] - L. Vu, D. Chatterjee, and D. Liberzon, ISS
of switched systems and applications to switching adaptive control
in Proceedings of the 44th Conference on Decision and Control, Seville,
Spain, Dec 2005, pp. 120-125. [The article may be found here.]
[Abstract: In this paper we prove that a switched nonlinear system has several useful ISS-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.] - D. Chatterjee, and D. Liberzon, Stability and
stabilization of randomly switched systems, (Submitted to CDC'06)
[Preprint may be found here,
together with a more complete version.]
[Abstract: This article is concerned with stability analysis and stabilization of randomly switched systems with control inputs. The switching signal is modeled as a jump stochastic process independent of the system state; it selects, at each instant of time, the active subsystem from a family of deterministic systems. Three different types of switching signals are considered: the first is a jump stochastic process that satisfies a statistically slow switching condition; the second and the third are characterized by exponential and uniform holding times, respectively, together with a stationary temporal probability distribution over the family of subsystems. For each of the three cases we first establish sufficient conditions for stochastic stability of the switched system when the subsystems do not possess control inputs; not every subsystem is required to be stable. Thereafter we design feedback controllers when the subsystems are affine in control and are not all zero-input stable, with the control space being general subsets of. Our analysis
results and universal
formulae for feedback stabilization of nonlinear systems for the
corresponding control spaces constitute the primary tools for control
design.]
- Stochastic Switching Systems: Analysis and Design, by El-Kébir Boukas, Boston: Birkhäuser, 2006. AMS Math Reviews. [I have NO idea why the pdf document obtainable via AMS MathSciNet shows H1 in place of H_\infty everywhere.]
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