Equivalent realizations for uncertain systems with an IQC uncertainty description

This paper considers uncertain systems in terms of their corresponding system input-output behavior. The paper develops a necessary and sufficient condition for the input-output behavior of a given uncertain system to be contained in the input-output behavior of another uncertain system. This result also enables one to consider the equivalence between two uncertain systems. The uncertain systems under consideration are linear time-varying uncertain systems in which the uncertainty is described by a time domain integral quadratic constraint.     

Robust controllability of linear stochastic uncertain systems

The paper extends the concept of robust controllability via linear state feedback to stochastic uncertain systems. We show that the controllability of a stochastic uncertain system can be characterized using solutions to a game-type differential Riccati equation.     

On the controllability of switching linear systems

This note presents a necessary and sufficient condition for small time controllability of a linear switching system (that is, a collection of linear time-invariant control systems, where a trajectory is any concatenation of trajectories of the individual systems). This result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.     

Stabilization of uncertain linear distributed delay systems with dissipativity constraints

This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials, trigonometric and exponential functions. By constructing a Liapunov–Krasovskii functional related to the distributed kernels, sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities (LMIs). In contrast to existing methods, the proposed scenario is less conservative or requiring less number of decision variables based on the application of a new derived integral inequality. Finally, numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology.     

Stochastic controllability of linear systems with Markovian jumps

The notion of stochastic controllability for linear systems subject to Markovian jumps in parameter values is studied. An algebraic necessary and sufficient condition is obtained in terms of an easily computable rank test.     

Exact observability and controllability for linear neutral type systems

The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllability problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.     

Stability and controllability of planar, conewise linear systems

This paper presents a fairly complete treatment of stability and controllability of piecewise-linear systems defined on a conic partition of . This includes necessary and sufficient conditions for stability and controllability, as well as establishing that controllability implies stabilizability by piecewise-linear state feedback. A key tool in the approach is the study of the Poincaré map.     

Necessary and sufficient condition for the controllability of switching linear hybrid systems

Controllability of switching linear hybrid systems by means of algebraic conditions was discussed by Yang (Automatica 38 (2002), 1221). This paper shows that algebraic conditions complemented with an assumption on the switching function provides not only necessary but also sufficient condition for the problem. The relation of these algebraic conditions with an invariant subspace algorithm is also presented.     

Global controllability of linear autonomous systems: A geometric consideration

The global controllability in finite time of a linear autonomous system with restrained controls is investigated. Necessary and sufficient conditions are obtained by an approach based on the consideration of geometric properties of the system.     

A stabilization algorithm for a class of uncertain linear systems

This paper presents an algorithm for the stabilization of a class of uncertain linear systems. The uncertain systems under consideration are described by state equations which depend on time-varying unknown-but-bounded uncertain parameters. The construction of the stabilizing controller involves solving a certain algebraic Riccati equation. Furthermore, the solution to this Riccati equation defines a quadratic Lyapunov function which is used to establish the stability of the closed-loop system. This leads to a notion of ‘quadratic stabilizability’. It is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable.The paper also deals with a notion of ‘overbounding’ for uncertain linear systems. This procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems. Also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process.     

Design of switching sequences for controllability realization of switched linear systems

In this paper, we study the problem of designing switching sequences for controllability of switched linear systems. Each controllable state set of designed switching sequences coincides with the controllable subspace. Both aperiodic and periodic switching sequences are considered. For the aperiodic case, a new approach is proposed to construct switching sequences, and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d(d-d₁+1). Here d is the dimension of the controllable subspace, , where (A_i,B_i) are subsystems. For the periodic case, we show that the controllable subspace can be realized within d switching periods.     

On the controllability of linear juggling mechanical systems

This paper deals with the controllability of a class of nonsmooth complementarity mechanical systems. Due to their particular structure they can be decomposed into an “object” and a “robot”, consequently they are named juggling systems. It is shown that the accessibility of the “object” can be characterized by nonlinear constrained equations, or generalized equations. Examples are presented, including a simple model of backlash. The main focus of the work is about linear jugglers.     

An algebraic approach towards the controllability of controlled switching linear hybrid systems

Based on the hybrid controllability concept (IEEE Automat. Control 43(4) (1998) 491), the controllability problem for a class of hybrid control systems referred to as controlled switching linear hybrid systems is discussed. One sufficient condition and one necessary condition are derived by employing algebraic manipulations of related system matrices. The computational test of these conditions and some examples are also discussed.     

Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

Popov–Belevitch–Hautus type controllability tests for linear complementarity systems

It is well-known that checking certain controllability properties of very simple piecewise linear systems are undecidable problems. This paper deals with the controllability problem of a class of piecewise linear systems, known as linear complementarity systems. By exploiting the underlying structure and employing the results on the controllability of the so-called conewise linear systems, we present a set of inequality-type conditions as necessary and sufficient conditions for controllability of linear complementarity systems. The presented conditions are of Popov–Belevitch–Hautus type in nature.     

Robust analysis and synthesis of linear time-delay systems with norm-bounded time-varying uncertainty

The problems of robust analysis and synthesis of systems with state-delay and norm-bounded time-varying parameter uncertainty are studied. It is shown that these problems are equivalent to the H_∞ analysis and synthesis problems of an auxiliary system, which is independent of the time-delay and the uncertainty in the system. The necessary and sufficient conditions for the equivalence are developed. Thus any standard H_∞ analysis and synthesis method can be used to solve this problem.