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The paper deals with the LPV stabilizability problem for linear plants whose parameters vary with time in a compact set. First, necessary and sufficient conditions for the existence of a linear gain-scheduled stabilizing compensator are given. Next, it is shown that, if these conditions are satisfied, any compensator transfer function depending on the plant parameters and internally stabilizing the...
We consider networks of input-to-state dynamically stable (ISDS) systems and provide a small gain condition under which the entire network is again ISDS. A Lyapunov formulation of the nonlinear small gain theorem for two interconnected ISDS systems is proved. It provides a constructive method to find an ISDS Lyapunov function for such an interconnection.
The robustness of quantized continuous-time non-linear systems with respect to the discrepancy (mismatch) between the ranges of the encoder and the decoder quantizers is investigated. A condition which guarantees asymptotic stability and which describes the interplay between quantization density and mismatch is derived.
A new small-gain theorem is presented for general nonlinear control systems described either by ordinary differential equations or by retarded functional differential equations. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability results. It is shown that the proposed approach recovers several recent results as...
This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixedframe measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose fully nonlinear pose observers based directly...
In multi-hop wireless networks, maximizing network utility by joint congestion control and scheduling has drawn much research interest, and significant progress has been made that has yielded much insight. However, in attempting to maximize network utilization, most scheduling mechanisms proposed in earlier works are too complicated to be implemented in wireless devices. One traditional approach to...
In this paper we study the characterization of asymptotic stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension...
This paper proposes a novel synthesis approach to dynamic output feedback robust model predictive control for systems with both polytopic description and bounded disturbance. The notion of quadratic boundedness is utilized to characterize the stability properties of the augmented closed-loop system. An error signal is defined, which is a linear combination of the true state, controller state and output...
Stability conditions for state-delay systems are derived based on the norm of semigroup, which describes the transition of the internal state. Introducing an exact calculation method of the semigroup norm, the conditions for the internal stability and the marginal stability are characterized by non-singularity of a transcendental function. The conditions depend on the existence of time interval such...
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
This paper investigates the existence and representation of stabilizing solutions to a class of generalized algebraic Riccati equation (GARE), which is often encountered in analysis and synthesis problems of continuous-time descriptor systems, such as H1 control and positive real control. The GARE under consideration consists of a couple of equations AT X + XT A + XT RX + Q = 0 and ET X = XTE ?? 0,...
Event-triggered and self-triggered control have recently been proposed as an alternative to periodic implementations of feedback control laws over sensor/actuator networks. In event-triggered control, each sensing node continuously monitors the plant in order to determine if fresh information should be transmitted and if the feedback control law should be recomputed. In general, event-triggered control...
We consider the problem of analysis and control of spatially invariant discretely distributed systems. It is well known that for certain types of subsystem models, the interconnected systems can be represented by infinite dimensional Laurent operators with rational symbols. Using Fourier techniques, the resulting analysis and control problems can be written as finite dimensional eigenvalue inequalities,...
In this paper we give conditions that a discrete time switched linear systems must satisfy if it is stable. We do this by calculating the mean and covariance of the set of matrices obtained by using all possible switches. The theory of switched linear systems has received considerable attention in the systems theory literature in the last two decades. However, for discrete time switched systems the...
The control of a new kind of airship is presented. By restricting its flight to a vertical plane, the mathematical model is reduced. The simplified model is proved to be minimum phase, and a nonlinear controller based on input-output linearization is designed. Since the performance of the controller is significantly impacted by the choice of parameters, simulations of three different pole placement...
This paper is concerned with the problem of receding horizon control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a nonlinear feedback policy with respect to noise measurements and show that the resulting mathematical program has a tractable convex solution. Moreover, under the assumption that the zero-input...
A recent paper proposed an MPC methodology which achieved a considerable reduction in the online optimization by transferring some of the computational load to calculations that can be performed offline. The approach was based on an augmented autonomous state space formulations of the prediction dynamics and gained significantly in efficiency by imposing a terminal constraint at current time. The...
This paper develops semistability analysis results for nonlinear switched systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. The main results of the paper involve sufficient conditions for semistability using multiple Lyapunov functions and integral-type inequalities.
Control performance is an important issue for model predictive control (MPC). For the aggregation based MPC controller, where the aggregation strategy is adopted to the control input sequence of MPC, the online computational burden is generally reduced at the cost of control performance. How to guarantee the control performance with the reduced online computational burden is a critical issue for applying...
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